Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton ON TAP HK I-MU, LOGARIT,LUY THUA1.NH NGHA LY THA V CN.S m C s a Ly tha a*N n R a n a a a a an( ...... . tha s )0 0 a10 a a) (*N n n 0 annaa a1 ) , (*N n Z mnm 0 > a) ( a b b a a a an n n mnm ) , ( lim*N n Q r rn n 0 > a nra a lim 2. TNH CHT CA LY THA.* vi a > 0, b > 0, ta c babab a ab a a aaaa a a ,_

+; . ) ( ; ) ( ; ; ..a > 1 : > > a a0 < a < 1 : < > a a3. NH NGHA LGARIT.* Vi s 0 , 1 0 > < b a.

b a ba log b e bb b ln10 log4. TNH CHT CA LGARIT. *b a aba aa log; 1 log ; 0 1 log*c b c ba a alog log ) . ( log +

c bcba a alog log log ,_

b ba alog . log c bit: bnb bbana a alog1log ; log1log *c c bbcca b aaablog log . loglogloglog c bit : b babaabalog1log ;log1log

c b c b ac b c b aa aa a< < > < > > >0 log log : 1 00 log log : 15. GII HN. 1) 1 ln(lim ; 11lim0 0+ xxxexxx6. BNG O HM.x xe e )' (u ue u e '. )' ( Trang 1Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton a a ax xln . )' ( xx1)' (ln a axxaln1)' (log ) 0 , 0 ( . )' (1> x x x n nnx nx11)' (a a u au uln . '. )' ( uuu')' (ln a u uualn .')' (log ' . )' (1u u u n nnu nuu1.')' (7 .CC DNG C BN CA PHNG TRNH , BT PHNG TRNH M V LGARIT.a)) ( ) ( 1 0) ( ) (x g x f a a ax g x f + +0 y 6 45 , 15 , 2 xx xyy y23) ( )( ) ( )l g l g5 l g l g l g6l g1l g 6 l g l g6o x y o o x o y oo xo y o y o+ + ' + +24) ( )' 1 l o g1 l o g l o g22x yxxyy xy25) ( ) ( )' +1 l o g l o g2 2y xy x y xy x26) ( )' + 9 l o g 2 43 662x y xxy x27) ( ) ( )' +21 l o g l o g2 22 2v uv u v u 28) ( )' 0 p q v q pyxyxy xaaaq pl o gl o gl o gTrang 8Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 14) ( )( )' + +y x y xy xx y5l o g 32 75315) ( ) ( )'+++ + 85 35 4 21 2y xy xy xy xx y x y16) ( ) ( )'> 0 x 6 4 222yyxx17) ' + +315 21 21l o gl o g2 252y xxyyx18) ( )'> ++ 0 x 811 0 72y xxy y19) ' +

,_

3 20 5 l o g 2 l o g 2212x yy xxy29) '

,_

+5 l o g l o g 2 21 212y xy xxy30) ( )'> 0 x 211 62 2y xxy x35) ( ) ( )l g l gl g4 l g33 44 3o x o yo ox y '36) ( )'< +0 a2 2 2 22l g 5 , 2 l g l g a y xa xy37) ' +1 l o g l o g44 4l o g l o g8 8y xy xx y38 ) ( )( )' + +1 3 7 , 01 21 6 2822x xy xy xxy xy x39) ' +1 l o g l o g2 7 23 3l o g l o g3 3x yy xx yPHNG TRNH V BT PHNG TRNH LOgrIT1.( ) ( )5 5 5log x log x 6 log x 2 + +2. 5 25 0,2log x log x log 3 + 3. ( )2xlog 2x 5x 4 2 + 4.2x 3lg(x 2x 3) lg 0x 1++ + 5.1.lg(5x 4) lg x 1 2 lg0,182 + + +6.1 214 lgx 2 lgx+ +32. 3 12log log x 0 _ ,33.134x 6log 0x+ 34.( ) ( )2 2log x 3 1 log x 1 + + 36. 5 xlog 3x 4.log 5 1 + > 37. 232x 4x 3log 0x x 5 ++ 38. 1 32log x log x 1 + > 39. ( )22xlog x 5x 6 1 + 40.( )23x xlog 3 x 1 >41. 223xx 15log x x 1 02+ _ + ,42. x 6 23x 1log log 0x 2+ _> + , 43. 22 2log x log x 0 + 44.x x2161log 2.log 2log x 6>45. 23 3 3log x 4log x 9 2log x 3 + 46. ( )2 41 2 162log x 4log x 2 4 log x + < 47. 26 6log x log x6 x 12 + 48. 32 22 log 2x log x1xx >49. ( ) ( )x x 12 12log 2 1 .log 2 2 2+ > 50. ( ) ( )2 32 25 112log x 4x 11 log x 4x 1102 5x 3x 51. +>+2331 log x11 log x 52. + < +5 51 215 log x 1 log x53. >x 1001log 100 log x 0254. 1 125 25< xlog x log55.( ) ( ) ( ) 0 4 2 2 133131< + + + x log x log x log56.( ) x log x logx2222 + 457. ( ) ( )2 25 5log 4 12 log 1 1 x x x + + x x x59. ( )38241 + x log x log 160.( ) ( ) 2 4 3 1 2 4 32329+ + > + + + x x log x x log61.( ) ( ) 1 1112 + > +x log x logxx62. ( ) ( )232 33 3234 3 2 8 2 x log x x x log x log x log x + + 63.2 2000 1 < +xlog64.01 3 255lg 2/.( ) ( )3 2 3 2 2x x+ + 3/. 2x + 2 + 5x + 1 < 2x + 5x + 24/. 3.4x + 1 35.6x + 2.9x + 1 05/. ( )( ) ( )22 12 1 2 2 1 . 2 5x x x ++ > + + 6/. 1 14 3.2 802 1x xx++ +7/. 22 4x x 8/. 3 1 3 2 3x x+ + 9/. 2x 1.3x + 2 > 36 10/. 2 2 11 2 5x x+ + Trang 12Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 11/. 19 4.3 27 0x x+ + 12/. 2 22 3 2 32 3x x x x 13/. 11 14 5.2 16 0x x x x + + + + 14/. 23 406xxx x+ > 15/. 16 4 2 2.3x x x ++ < +16/. 1 1 1 2 2 2 9x x+ + 0, h phng trnh sau c nghim duy nht:( ) ( ) ln 1 ln 1x ye e x yy x a + +' D. BT PHNG TRNH H PT LOGARIT.Bi 1: Gii cc bt phng trnh: 1/.( ) ( )2 4 4 2log log log log 2 x x + 2/. 2 2log 3 log 1 x x + +3/. ( )( )22 2log 3 2 log 14 x x x + +4/.( )22 23log 2 log 1 x x 5/. ( ) 2 1log 4 2x xx+ 6/. ( )2 22 2log 2log 3 5 4 0 x x x x + + 7/. 2 2log 1 3 log x x 8/. 22log12log2 2. 3xxx + 9/. ( )( )222log 6 52log 2x xx +10/. 22 22log log 20log2x xx 11/. 2 1 122log log log 3 1 x x _ + ,12/. 22 3 3 2log .log 2 log log x x x x + +13/. 22 2log log 18xxx _+ ,14/. 233log log3 6x xx + Bi 2: Gii cc h phng trnh 1/. 2 26log log 3x yx y+ '+ 2/. ( )2 223 3log 6 4log log 1x yx y+ + '+ 3/. log log 26y x y xx y+ '+ 4/. 2 226log 3log log 2x yx y+ '+ 5/. ( ) ( )2 23 53log log 1x yx y x y '+ 6/. 22log 42 log 2x yx y+ ' Trang 14Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 7/. 23loglog 2 39yyxx+ ' 8/. 2 22 2log log16log log 2y xx yx y + ' 9/. ( )( )log 2 2 2log 2 2 2xyx yy x+ '+ 10/. 2 224 2log log3. 2. 10log log 2y xx yx y+ '+ 11/. 32log 4yxyx ' 12/. ( )22log 4log 2xyxy ' _ , Trang 15Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton bin i mBi1: Rt gn biu thc:A = 221211212113 43 29 4111]1

+ +a aa aa aa avi 0 < a 1, 23B = 3 262 312 1 32 . 2aa a a a

,_

+2C = 221 11 2xx ab +vi x = 21

,_

+abbaa, b < 0D = ( ) ( )( )31 2 22 121 2 b a b ab a ab baE = ( )

,_

+++ 1 11 11 11 11 141b ab ab ab aab b a vi ab 0, a t bF = b ababaabnnnnn 11G = ) )( )( () )( (212141414141343231323231b a b a b ab b a a b a+ + + + vi a, b > 0 H = 1 1 12 2 21 12 22 2 1.12 1a a aaa a a _+ + + + , I = 32 3323222 3323223 6 4 2 2 4 622 ) (2 ) (3 31111]1

+ ++ + + +b b a ab b a ab b a b a aaK = ab ababaababb ab a ab++ +

,_

++2 1.1244 3 4 3vi a, b > 0 v a b Bi2: Rt gn cc biu thc sau:A =( )111+xxx B =( )2164xxx C =+ + 1 2 x x 1 2 x xD =( )( )14 2243 21 22 31 1211]1

+ ++ ++ x xx xx xx E = 1 ) 2 2 (4111 ) 2 2 (41122+ + +x xx xF = x a x ax a x a + + +vi x = 122+ babG = 11 222 +x xx a vi x =

,_

+abba21a, b < 0Bi3: Rt gn cc biu thc sau:A =( )2 42 a a B =( )4 4 8b a a + C = 2 22 2b a a b a a + +D=

,_

++ abbab aab4112 vi a, b > 0 E = 2 22 2b a a b a a +Bi4: Bin i cc biu thc sau v dng lu tha c s a, bit:A = 7 5 33 3 3 3v a = 3 B = 3542 4va =2Bi5: so snh a, b bit:a) b a >b) ( ) ( )b a2 5 2 5 + >

bin i logaritBi1: Tnh gi tr ca biu thc sau:Trang 16Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton A = ( )52153128 2 22 2 log927log 62 log 9 8 log + B = 27 log 3 log 2 4 log 18 log 6 log125 2 97 55 4 33 49 25+ + + +C = 42 236 log 2 log 1 5 log2 log log3 5 369 5 6 +D =5 log 2 log3 log 23313221 92343 27 log 2 16 4 log++ Bi2: Rt gn biu thc: A = 3 log22 log18 63 4 + B = 3 log12 log18 632 9 +C = ( )217 log 5 log8 649 25 +Bi3: Tnh gi tr ca cc biu thc sau:a) A = 62log abit 218 log ab) B = abb a22 log bit logab = 2c) C = 32 log9bit log26 = a d) D = 16 log30 bit a = lg3v b = lg5Bi4: Cho m = 3 log2 v n = 5 log2. Tnh theo m v n gi tr ca cc biu thc: A = 62135 logB = 623 , 0 log C = 103log30D = 2250 log2E = 62360 logBi5: Cho a = 18 log12vb = 54 log24.CMR: ab + 5(a - b) = 0Bi6: Chng minh rng: vi 0 < a, b, c, abc 0 lun c:

dd d dd d d d d dabcc b aa c c b b aloglog . log . loglog log log . log log . log + +Bi7: Cho 0 < x1, x2, , xn 1. Chng minh rng:

1 log log .... log log log1 4 3 21 3 2 1x x x x xn nx n x x x xBi8: Cho 0 < x1, x2, , xn 1. Chng minh rng:

a a aannx x xx x xlog1...log1log11log2 12 1...+ + +Bi9: Chng minh rng vi c b az y xlog , log , log theo th t lp thnh mt cp s cng ta lun c:z xz xyc ac ablog loglog . log 2log+, 0 < a, b, c, x, y, z 1Bi10: Chng minh rng vi 0 < N 1 v a, b, c theo th t lp thnh mt cp s nhn ta lun c: N NN NNNc bb acalog loglog logloglog,0 < a, b, c 1Bi11: Chng minh rng vi x2 + 4y2 = 12xy; x, y > 0 ta lun c: ( ) ( ) y ln x ln ln y x ln + +212 2 2Bi12: Choxaa ylog 11; z = yaalog 11. Chng minh:x = zaalog 11

Bi13: Xc nh a, b sao cho:( ) b a b a + +2 2 2log log logph ng trnh v bt ph ng trnh m i) ph ng php logaritho v a v cng c s 1) 500 8 . 51xxx HKTQD - 982) ( ) ( ) 2 4 4 2 4 22 21 + + x x x xx H M - D - 20003)132.3+x xx x222T) M B khi - 2001 - HSPI ( , ,Trang 17Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 4) ( ) ( )5 51 x1 - x1 - x+ + 2 22001 - Vinh thutSP k ng (Cao5)1 1 - x2x+ 3 4x A) khi - 2001 - Nai ng SPng (Cao6) ( ) ( )31133 10 3 10++ < +xxxxHGT - 987) 2 45 22 x x8) 122212xx x9) 2 1 2 14 4 4 9 9 9+ + + ++ + < + +x x x x x x10) 1 3 1 22121+ +x x11) ( ) 1 1 2112 + +xxx x12)( )32221 12 > +x xx x13) 2 4 3 15 3 5 3 . 7+ + + ++ +x x x xIi) t n ph:1) 1 4 4 47 3 2 5 6 2 32 2 2+ ++ + + + + x x x x x x HVQHQT - D - 992) ( ) ( ) 4 3 4 7 3 4 7sin sin + +x xHL - 983) ( )1212212 . 6 21 33 + x xx xHY HN - 20004)( ) 0 5 2 3 2 . 2 9 + + x xx xHTM - 955)( ) 7 7 , 0 . 610072+ xxxHAN - D - 20006) 11 231331+

,_

+

,_

x x= 12 HVCTQG TPHCM - 20007) 1231331 x2x2>

,_

+

,_

+12001) - TPHCM HY (8) 10 9 92 2cos sin +x xHAN - D - 999) 1 1 24 2 2 12x x x + + ++ +HTCKT - 9910)2 22 1 2 22 9.2 2 0x x x x + + + + HTL - 200011) ( ) ( )( ) ( ) 3 2 4 3 2 3 4 7 3 2 + + + +x xHNN - 9812) 0 6.3 - 1 -7.3 5.31 x x 1 - x 1 - 2x + ++9A) khi - 2001 - c hng H (13) 0 6.9 13.6 - 6.4x x x +2001) - dong nh b lp dn H ( i14)3 2.3 - 9x x + + + x x x xHGT - 9822)0 2 264 3 1 2 + + x x23) ( ) ( ) 4 3 2 3 2 + + x x24) ( ) ( ) 0 2 3 2 3 3 4 7 + +x x25) 1 1 12 2 29 6 4 . 2+ + + +x x x26) 1 2 . 2 2 25 6 1 6 52 2+ + + x x x x27) 10 16 162 2cos sin +x x28)01 21 2 21+ xx x29) x x x x2 2 . 15 25 3 6 3 2< + + +30) 2 2 22 2 1 2 15 . 34 9 25x x x x x x + + +Trang 18Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 31) 0 3 . 18 31loglog323> + xxx33) 3 log211249131>

,_

,_

x x34) 9 3 3 92 > + x x x35) x x x x9 9 3 . 84 41> ++ +36) 1 3 1 32 23 . 28 3 9 + < +x x37) 0 1 3 . 4 3 . 42 12 + + x x x38) 25221221log log> +x xx 39) 0 1 2 42 12 + + + + x x xIII) ph ng php hm s: 1) 1 22 10 25+ +x x xHVNH - D - 982) x x x9 . 3 6 . 2 4 HVL - 983) 26 . 5 2 . 9 3 . 4xx x HHH - 994) 1 32 50 125+ +x x xHQG - B - 985)( )2 - 22121 xx x x) 2001 - li Thu H (6) ( )x 2 2 23 2x 3x - .2x 3 2x 3x - + + > + + 2 5 2 5 x xx 2001) - nh b thi HY ( i7) 1 6 3 . 3 2 . 2 > +x x xHY - 998)xx3 8 12 +9) 5 log log 22 23 x xx +10)( ) 0 3 3 10 3 32 3 2 + + x xx x11)( )2 11 2 22 + xx x x 12) 13 2 34 2 4> ++ + x x13)02 42 3 32 +xxx14) 3x + 5x = 6x + 2Mt s bi ton t luyn:1) 3x+1 + 3x-2 - 3x-3 + 3x-4 = 750 2) 7. 3x+1 - 5x+2 = 3x+4 - 5x+3 3) 6. 4x - 13.6x + 6.9x = 0 4) 76-x = x + 25) ( ) ( ) 4 3 2 3 2 + + x x ( 52/III1)6) 1 3 22 + xx( 70/II2)7) 3..25x-2 + (3x - 10)5x-2 + 3 - x = 0 ( 110/I2) 8) ( ) ( )xx x2 3 2 3 2 + +9)5x + 5x +1 + 5x + 2 = 3x + 3x + 3 - 3x +1 1( )( ) ( ) ( )2 1 2 12563 1 81 221 4 3 33 3 3 2 2 2 20 2 16 2 19 4 2 184 1 15 17 10 24 5 24 5 16 0 4 6 6 13 9 6 150 4 5 5 14 3 36 8 12 4 2 11 1 1 10222 + + + + + + + + + + + + +x x x x x xx xx x xxx x xx x xx x xxxx x x xx) ) )) ) . . . )) . ) ) )

( ) ( )( ) 0 17 2 2 ) 26 0 27 3 . 4 3 ) 25 1 2 2 ) 241 ) 23 1 1 ) 22 12 5 . 3 . 2 ) 217 6 2 5 2 8 4422212 2 122 + + + + + + + + x x x xxxxx x xx xx x x x

( ) ( ) 0 8 4 . 15 16 . 2 ) 28 0 4 3 2 3 2 ) 27 + +x xx x

( ) ( ) ( ) ( )32 5 3 16 5 3 ) 30 0 2 3 2 3 3 4 7 ) 29+ + + + +xx x x x 0 12 2 8 33 9 6 4 2 32 36 5 81 2 16 3 313 3 2 1 1 1 + + ++xxx x x xx x x) . ) . . . ) ( ) ( )( )( )( )31 - x x x7 - 3x3 - xx 21x 45xx 2x 1x10 0,01. .5 242)1 8 41)0 16 - .0,5 2 40)2 4 2 39)8131. .3 3 38)

2 2

,_

+ + + + + + + ++++ +++ + + 3 3311 3110 3311 2 22 1 1 2 2 1 225 , 0125 , 0 . 40 2 1 2 2 3 ) 375 3 2 5 3 2 ) 36 0 4 3 ) 35 5 4 3 ) 34xxxxxxx xx x x x x x x x x xx xxTrang 19Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton x x1 12 1 11250 . 25 , 4 25 +

,_

,_

+ x11 - x 1 - 2xx x x x3 xx10 46) 0,2 2.5 - 3.5 45)2 - 3 3 - 2 44)125279250,6 43)2 2 2 220 24 - 10.2 - 4 48)0 3 36.3 -9 47)1 - x x x x2 2 + 3 1ph ng trnh v bt ph ng trnh logarit I) ph ng php m ho v a v cng c s: Gii cc ph ng trnh v cc bt ph ng trnh sau: ( ) ( )3 21 331) log 2 x x 2 log 2x 2 0 1+ + + ]( ) [ ] { }212log log 2)3 4 + + x2 2log 3 1 log 1( ) ( ) 1 - x log x log 3)2122 1( ) 3 x log 4)2x + 4 4x1 2 4.log log 5) 2coscosxx( ) ( ) 1 + + x3222x 2log 1 - x log 6)x log x log x log 7)5 4 3 +( ) ( ) ( )3 218) log x 8 log x 58 log x 4 42x + + + + +( ) ( ) ( )6 x log x - 4 log 3 - 2 x log239)341341241+ + + 10)( ) ( ) ( ) ( ) 1 log 1 log 1 log 1 log2 422 422222+ + + + + + + + x x x x x x x x11)( ) ( ) 1 1 2 log . log log 23 329 + x x x12)( ) ( ) 3 log 3 12 7 log 2 3 log22222+ + + + + + x x x x13) x x x x10 4 3 2log log log log + +14) ( ) 3 6 log + xx15) 1 23 2log3

,_

xx16)( ) ( )382244 log 4 log 2 1 log x x x + + + +17)( ) ( ) ( ) 9 3 . 11 log 3 3 log 3 log 1515 5 + + + x xx18)( ) ( ) 11 4 log 16 log222 x x19)( ) ( ) 2l g 1 . 5 l g 5 1 o x o x 1 > + ]20) 1 2 log3< x21)113 2log3 +x24)( ) 2 3 8 5 log2> + x xx25) 011 3log2>+xxx26)( )( ) 1 2 loglog5 , 05 , 022 508 , 0

,_

xxxx HD: 0,08 = 2 222 552252

,_

,_

27) ( )32 2222log log +x xx28) ( )331311 1 log log21 + < x x29) 241log

,_

xx30) ( ) 1 2 loglog1133 512 , 0

,_

xxxx31) 2 2004 log 1 < +x32) ( )( )35 log35 log3>xxaa33)( ) 0 ) 1 2 ( log 32 2 . 12 42 + xx x34) 2122 4log 2

,_

xxx35) ( ) 1 log11 3 2 log131231+>+ xx x36) xxxx22122322142log 432log 98log log + + x x xTrang 20Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 38) ( ) [ ] 0 5 log log2421> x39)( ) 1 6 522< + x xxlog40) 1 52log3 x x43) ( ) 2 2 l o g 1 l o g222 < + x xII) ph ng php t n s ph: Gii cc ph ng trnh: x2lgxx xlg 229lg 310 ) 12 ( )( ) [ ]( )3 log2 - x 9 2 - x 2)32 9x( ) ( )2 2.3 .log 3 log 3)x2x2 2 1( ) lg6 xlg5 2 1 lg x 4)x+ + +( ) ( ) ( ) 1 1 1 + 262322x - x log x x .log x - x log 5)( ) ( ) ( )0 5x - x lg x x lg 6)2 2 2 2 2 + + + 1 5 1( ) [ ] ( ) 0 2 - x log 1 - x x log 7)22 2 + x2( ) ( ) 6 log - 5 2 log 3 8)2 2 + + + + 5 4 5 42 2x x x x1 log x log 9)222 + + 1 x10)( ) ( ) 1 5 5 log . 1 5 log125 5 + x x11) ( )( ) [ ]( )3 1 4 log1 8 12 x xx12)( ) ( ) 2 2 5 . 2 log . 1 5 log2 2 x x13) 6 33 log log2 2 + xx14) 3 4 log 2 log2 2 + xx15)( ) 0 5 6 2 log 1 2 log2222 + + x x x x x16)( ) 0 3 2 log 2 2 5 log2 52> + ++xx17) 0 3 18 321loglog323> + xx18)( ) 0 2 2 log 1 log222> + + x x x x19) 4log log log . log223 2 3xx x x + +x xx21) ( )6 3323log log +x xx22) ( )34 15log 4 1 log 32xx++ + >23)x x2 2log log 2 > III) ph ng php hng s bin thin: 1) Gii phng trnh: 0 9 lg 9 lg 2 lg lg2 3 4 + x x x x2) Cho phng trnh:( ) ( ) ( ) 0 1 lg 1 lg 2 lg 1 2 lg2 2 3 4 + + + + m x m m x m m x m xa) Gii phng trnh vi m = -1.b) Xc nh m phng trnh c bn nghim phn bit.IV) S dng tnh n iu (ng bin hoc nghch bin):Gii cc phng trnh: 2 2 x logx2 + + 2 ) 11232)x+ + x2log 1( ) ( ) [ ] 2 x 8 log x x log 3)222+ + 4( ) 0 6 2x - x log 5 - x x log 6)222 + +( ) x log 3 x log 7)6log26 +x( ) x 2 8)2log+1 x4)( ) ( ) 3 2 log 2 2 log22254 x x x x5) 5 log log 22 23 x xx +Trang 21Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 9)( ) 0 3 log 4 log323 + + x x x x8) Gii v bin lun phng trnh: ( )2 22 12log 3 2 log 3 2 x x x m x m x x + + +10)( ) ( )2l g 6 l g 2 4 o x x x o x + + +11) ( )xx+3 log5212)( ) ( ) 1 log 2 log2 3+ + x x13)( ) 1 log log2 3+ x x14)( ) ( ) 3 2 log 2 2 log23 223 2 2 ++x x x x16)( ) x x732log 1 log +18)( ) x x x48 46log log 2 +19)( ) 2 log log3 7+ x x20) 12 7712log223 + x x xxx x21)( ) 0 3 log 2 log2 22> + + x x x x17)( ) ( ) ( ) ( ) 0 16 2 log 2 4 2 log 3323 + + + + + x x x xh ph ng trnh m v h ph ng trnh logarit Gii cc h phng trnh:1) ( ) ( )2 2log 5 logl g l g41l g l g3x y x yo x oo y o + ' 2) ( ) ( )3 34 32log 1 logx yy xx y x y+' + 3) '+ 511 0 5 1 52xyyx x4) ( )' ++3 2 3 l o g2 l o g1yyxx5) ( )( )' + +y xx yy xy x226 91 2226) ' 1 2331 l o gyxx y7) ( )2 449 27.3 01 1l g l g lg 44 2xy yo x o y x '+ 8) ( )' +2 l o g1 1 5 2 2 . 35y xy x9) ( )( ) ( )2 2l g 1 l g8l g l g l g3o x y oo x y o x y o + +'+ 10) ( )' 2 l o g9 7 2 2 . 33y xy x11) ( )( ) ( ) ( )'+ +x y x y x yx y5 5 5l o g 2 1l o g l o g 1 2 2 l o g 24 8 3312)( ) ( ) ( ) y x y x y x + +32 233 39log log log13) ( )' + +0 2 0 21 l o g 2 l o g l o g1 8a y xa y xa a14) ( )( )' + +y x y xy xx y5l o g 32 753Trang 22Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 15) ( ) ( )'+++ + 85 35 4 21 2y xy xy xy xx y x y16) ( ) ( )'> 0 x 6 4 222yyxx17) ' + +315 21 21l o gl o g2252y xxyyx18) ( )'> ++ 0 x 811 0 72y xxy y19) ' +

,_

3 20 5 l o g 2 l o g 2212x yy xxy20) ( ) ( )1l g 3 l g 5 04 4 8 8 0yx y xo x o y ' 21) ( )( )' + +2 3 2 l o g2 2 3 l o gy xy xyx29) '

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+5 l o g l o g 2 21 212y xy xxy30) ( )'> 0 x 211 62 2y xxy x31) ( )' +2 l g l g l g1 l g2x yy x32) ' 32 2 . 7 432x yyyxx33) ' +6 8 9 2 52 0 0 2 . 52 233y xy x34) ( )2 21l g 1,522210 100 1010 632 10 9o x yx yx y+ +'+ + 22) ( )'> + +0 y 6 45 , 15 , 2 xx xyy y23) ( )( ) ( )l g l g5 l g l g l g6l g1l g 6 l g l g6o x y o o x o y oo xo y o y o+ + ' + +24) ( )' 1 l o g1 l o g l o g22x yxxyy xy25) ( ) ( )' +1 l o g l o g2 2y xy x y xy xTrang 23Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 26) ( )' + 9 l o g 2 43 662x y xxy x27) ( ) ( )' +21 l o g l o g2 22 2v uv u v u28) ( )' 0 p q v q pyxyxy xaaaq pl o gl o gl o g35) ( ) ( )l g l gl g4 l g33 44 3o x o yo ox y '36) ( )'< +0 a2 2 2 22l g 5 , 2 l g l g a y xa xy37) ' +1 l o g l o g44 4l o g l o g8 8y xy xx y38 ) ( )( )' + +1 3 7 , 01 21 6 2822x xy xy xxy xy x39) ' +1 l o g l o g2 7 23 3l o g l o g3 3x yy xx y40) ' ++4 25 2 2y xy x41) 'yyxx5 21 0 842) ' + 0 4 50 l o g l o g 5 , 02 22 2y xy x43) '1 62l o gl o gyxxyyx44) ' + + +2 285 1 2l o g l o gl o g l o gl o g l o gz xy xz zx zz zy yy zx yz x45) ( )' + ++ +1 1222x xyy x46) ' +129 9y xy xy x y x47) '1 8 2 . 31 2 3 . 2y xy x48) ( )( ) ( )' + + + 1 1 12 3 92 23 l o g l o g2 2y xx yx y49) 2cot sinsin cot9 39 81 2x yy gx+ ' Trang 24Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 50) ' +2 2 21y xy x51) '+ + + ++ +1 1 32 . 3 2 223 2 1 3x x y xx y y x52) ( )' 1 2 l o g . l o g35 , 2l o gx y yx y xyxyph ng trnh v bt ph ng trnh m cha tham s I) ng dng ca nh l o v du ca tam thc bc hai: (So snh s vi cc nghim ca phng trnh bc hai)1) Gii v bin lun phng trnh:( ) ( ) ( ) 0 1 2 2 . 5 2 . 2 + + m m mx x2) Gii v bin lun phng trnh: ( ) ( )32 5 3 5 3+ + +xx xa3) Xc nh m phng trnh sau c nghim: ( )( )( ) 0 6 2 2 . 1 2 2 21 1 22 2 + + + +m m mx x4) Tm m phng trnh:( ) ( ) 0 1 4 . 1 2 16 . 3 + + + + m m mx x c hai nghim tri du5) Cho phng trnh: 0 2 2 . 41 + +m mx xa) Gii phng trnh khi m = 2.b) Tm m phng trnh cho c hai nghim phn bit x1, x2 sao cho x1 + x2 = 36) Gii v bin lun phng trnh:a) 8 3 . 3 . +x xm mb)( ) 0 2 . 2 . 2 + + m m mx x7) Xc nh m cc phng trnh sau c nghim: a)( ) ( ) 0 3 3 3 2 3 12 + + + m m mx xb)( ) ( ) 0 1 2 2 2 4 4 + m m mx x8) Cho phng trnh: x x xm 36 . 5 81 . 2 16 . +a) Gii phng trnh vi m = 3b) Tm m phng trnh c nghim duy nht.9) Cho phng trnh: ( ) ( ) mtgx tgx + + 2 2 3 2 2 3a) Gii phng trnh vi m = 6.b) Tm m phng trnh c ng hai nghim ,_

2;2 .10) Xc nh m bt phng trnh:( ) 0 5 2 . 1 2 4 . < + + m m mx x nghim ng vi x < 011) Cho bt phng trnh: ( ) 0 4 1 16 6 9 .3 2 3 2 32 2 2< + + + x x x x x xm m(1)a) Xc nh m mi nghim ca (1) tho mn bt phng trnh 1 < x < 2(2)b) Xc nh m mi nghim ca (2) u l nghim ca (1).12) Xc nh cc gi tr ca m bt phng trnh:

( ) ( )x x x x x xm m + + 2 2 22 2 24 1 6 1 2 90 nghim ng vi mi x tho mn iu kin 21 x13) Cho bt phng trnh:( ) 0 1 2 4 11> + + + +m mx xa) Gii bt phng trnh khi m = -1.b) Tm m bt phng trnh nghim ng vi mi x.14) Cho bt phng trnh:( ) 0 1 2 41> + x xma) Gii bt phng trnh khi m = 916.b) Tm m bt phng trnh nghim ng vi mi x.Trang 25Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 15) Xc nh m bt phng trnh:a)( ) 0 1 2 1 4 .2> + ++m m mx x nghim ng vi x.b)3 2 . 4 + + m mx x 0 c nghim.c)( )x x xm m m 4 . 6 1 2 9 . + + 0 nghim ng vi x [0; 1]16) Cho bt phng trnh: 1231311 2>

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x x(1)a) Gii bt phng trnh (1)b) Xc nh m mi nghim ca (1) cng l nghim ca bt phng trnh: 2x2 + (m + 2)x + 2 - 3m < 0II) ph ng php iu kin cn v gii cc bi ton m cha tham s: 1) Tm m phng trnh sau c nghim duy nht: 1 2312 mx2) Tm m hai phng trnh sau tng ng:0 4 3 912 2 ++ x x1 4 . 2 . 41 2 + x xm m3) Tm m hai phng trnh sau tng ng: 16 2 2 42 4 1+ ++ + + x x x 1 9 . 3 . 91 2 + x xm m4) Tm m phng trnh sau c nghim duy nht: 2 3212 mxph ng trnh v bt ph ng trnh logarit cha tham s I) ng dng ca nh l o v du ca tam thc bc hai: 1) Xc nh m phng trnh sau c hai nghim dng:( ) ( ) ( ) 0 1 2 2 log 5 3 3 log .3 32 + + ++m m m xx2) Xc nh m phng trnh sau c hai nghim phn bit ,_

2 ;21: ( ) ( ) ( ) 0 1 2 6 2 2 2222log log + + m x m mx x3) Xc nh m bt phng trnh: mxx1 loglog2222 nghim ng vi mi x > 0CHUYN :PHNG TRNH-H PHNG TRNH V BT PHNG TRNH M V LOGARITI/ PHNG TRNH M V LOGARITBi 1: Gii Phng Trnh:.Trang 26Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton .Bi 2: Gii phng trnh sauBi 3: Cho phng trnh :vi m l tham s. Xc nh m phng trnh cho c nghim. Bi 4: Cho phng trnha)Gii phng trnh vi m=32b)Tm m phng trnh c 2 nghim phn bitBi 5: Giai phng trnh.

Trang 27Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton .II/ H PHNG TRNH M V LOGARITBi 1: Gii H Phng Trnh sau:. Trang 28Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton

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Bi 2: Tm m h phng trnh c nghim : Bi 3: Cho h phng trnh:1. Gii h vi m=2.2. Tm m h cho c nghim.Bi 4: Chng minh rng vi a>0 th h c nghim duy nht Bi 5: Gii h phng trnh sauIII/ BT PHNG TRNH M V LOGARITBi 1: Gii cc bt phng trnh sau .Trang 29Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Bi 2: Tm tt c cc gi tr ca a bt phng trnh sau c nghim ng vi mi x: .o hm ca hm s m v logaritBi 1: tnh o hm cc hm s sau:1, ( )22 2xy x x e +; 2,( )22xy x xe +; 3, 2.sinxy e x ;4, y = 22x xe+5. y = 1x x3x e .; 6. y = 2x x2x xe ee e+;7. y = x x2 ecos.;8. x23yx x 1 +;9. y = cosx.cotxe 10. y = 24x xe+; 11. y = x.13 x x4e ;12. y = 3x 2x3x 2xe ee e+,14. y = x x4 ecos.;15. y = x23x x 16. y = 2x2x e cos .1. y = ( )22x x 3 ln + + ;17. y =( )2x log cos ;18. y = ( )xe x .ln cos19. y =( )( )22x 1 3x x ln + ;20. y = ( )312x x log cos ;21. y = ( )2x 12x 1ln ++22. y = ( )2x 3x 1 ln + + ;23. y =( )3x log cos ;24. y = ( )( )22x 1 3x 2 ln + +25. y = ( )2123x x log cos +;26. y = ( )2x 1x 1ln ++;27. y = ( )2xe x .ln cos; 28,1 ln xyx x +29,cos sinlncos sinx xyx x+Bi2:1, cho( )2xef xx tnh( )'1 f;2, cho ( )2x xe ef xtnh( )'0 f; 3,cho( )2ln f x x tnh( )'f e;4; cho( ) ( )4ln 1 f x x + tnh( )'1 f ; 5,cho( ) ln sin 2 f x x tnh '8f _ ,; 6,cho( )sin2xf x e tnh( )'0 f7, cho( ) ln tan f x x tnh '4f _ ,;8, cho( )2cos xf x e tnh( )'0 f9,cho ( )112xxf x+tnh( )'0 f; 10,cho( ) ( ) ( ) tan , ln 1 f x xg x x tnh ( )( )''f xg x11,cho( )( )2ln 1 f x x x + + tnh( )'0 f; 12.cho( ) 2 .3x xf x tnh ( )'0 f13, cho( ) .xf x x tnh ( )'1 f; 14,cho ( )( )212logxf x+tnh( )'1 f ; 14,cho( )2lg f x x tnh( )'10 f ; 15, cho( )2xf x e tnh( )''0 fTrang 30Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 16, cho( )2ln f x x x tnh( )''f e;Bi 3:1, cho '1ln : 11yy cmr xy ex _ + + , ; 2,cho ( )2' 22. : 1xy x e cmr xy x y 3,cho[ ]'1: ln 11 lny cmr xy y y xx x + + ; 4: cho( )'1 :x xy x e cmr y y e + 5,cho 4 ''' '2 : 13 12 0x xy e e cmr y y y + ;6,cho 2. .x xy a e b e + cmr:'' '3 2 0 y y y + + 7,cho '' '.sin : 2 2 0xy e xcmr y y y + + ;8; ,cho ( ) 4.cos : 4 0xy e xcmr y y + ;9,cho sin xy e cmr:ycosx-ysinx-y=0; 10,2.sin5xy e x cmr:y-4y+29y=011,cho 21.2xy x e cmr:y-2y+y=xe ; 12, ( ) ( ) sin ln cos ln y x x +cmr: y+xy+x2.y=013,cho y=x3.lnx gpt: ( ) ( )1' 0 f x f xx+ ;cho( ) ( )23 1xf x e x x + +gpt: ( ) ( ) ' 2 f x f x 15,cho( )2 1 1 22. 7 5x xf x e e x + + gpt ( ) ' 0 f x ;16,cho( ) ( ) ( ) ( ) ln 7 ; ln 1 f x x x g x x + gbpt ( ) ( ) ' ' f x g x >17,cho( ) ( )2 11.5 ; 5 4 ln52x xf x g x x+ +gbpt ( ) ( ) ' ' f x g x + + + +m mx xa) Gii bt phng trnh khi m = -1.b) Tm m bt phng trnh nghim ng vi mi x.14) Cho bt phng trnh:( ) 0 1 2 41> + x xma) Gii bt phng trnh khi m = 916.b) Tm m bt phng trnh nghim ng vi mi x.15) Xc nh m bt phng trnh:a)( ) 0 1 2 1 4 .2> + ++m m mx x nghim ng vi x.b)3 2 . 4 + + m mx x 0 c nghim.c)( )x x xm m m 4 . 6 1 2 9 . + + 0 nghim ng vi x [0; 1]16) Cho bt phng trnh: 1231311 2>

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x x(1)a) Gii bt phng trnh (1)b) Xc nh m mi nghim ca (1) cng l nghim ca bt phng trnh: 2x2 + (m + 2)x + 2 - 3m < 0II) ph ng php iu kin cn v gii cc bi ton m cha tham s: 1) Tm m phng trnh sau c nghim duy nht: 1 2312 mx2) Tm m hai phng trnh sau tng ng:Trang 32Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 0 4 3 912 2 ++ x x1 4 . 2 . 41 2 + x xm m3) Tm m hai phng trnh sau tng ng: 16 2 2 42 4 1+ ++ + + x x x 1 9 . 3 . 91 2 + x xm m4) Tm m phng trnh sau c nghim duy nht: 2 3212 mxBai 1. A-02Cho phng trnh0 1 2 1 log log2323 + + m x xa) Giai phng trnh khi m = 2b) Tm m e phng trnh co t nhat mot nghiem thuoc oan[ ]33 ; 1Bai 2.B-02 Giai bat phng trnh1 )) 72 9 ( (log log3 xxBai 3.D-02Giai he '++ +yy yxx xx2 22 44 5 212 3Bai 4. Giai bat phng trnh) 2 . 3 2 ( log ) 4 4 ( log1 22121x x x ++Bai 5.Giai phng trnh) 4 ( log ) 1 ( log41) 3 ( log212842x x x + +Bai 6. Giai he ' + 0 l o g l o g0 3 | | 42 4y xy xBai 7. Tm k e he phng trnh sau co nghiem:' +< 1 ) 1 ( l o g31l o g210 3 132223x xk x xBai 8. Giai phng trnh160 log 3 log23273 x xxxBai 9. Giai he ' + +3 ) 5 3 2 ( l o g3 ) 5 3 2 ( l o g2 3y2 3xx y y yy x x xBai 10.Giai he ' +3 2 2l o g l o gx yy xy x yTrang 33Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Bai 11. Giai bat phng trnh1 12 1 2 1 2 . 15+ ++ +x x xBai 12. Tm m e phng trnh 4(0 log ) log2122 + m x x co nghiem thuoc khoang (0;1);Bai 13. Giai bat phng trnh 0 6 log ) 1 ( log 2 log24121 + + x xBai 14. D-03Giai phng trnh2x x 2-222 x x +=3Bai 15.Cho ham so f ) ( x = x.2 logx(x>0,x 1 )Tnh f) (xva giai bat phng trnh f ) ( x 0 Bai 16. Giai phng trnh xx 1 ) 4 5 ( log5Bai 17. A-04Ghpt ' + 2 511l o g ) ( l o g2 2441y xyx yBai 18. B-04 Tm gia tr ln nhat va nho nhat cua ham so y=x x2ln tren oan[ ]3; 1 eBai 19. B-05Ghpt ' + 3 l o g ) 9 ( l o g 31 2 13329y xy xBai 20.Gbpt 3 log log3 xx >Bai 21.Gbpt 2 .xx2log21x2log232 Bai 22.Tm m e phng trnh sau co 4 nghiem phan biet: 0 log 622 4 m x xBai 23. A-06 Giai phng trnh 3.8x + 4.12x 18x 2.27x = 0Bai 24. Giai bat phng trnh logx+1(-2x) > 2Bai 25.Giai phng trnh : 0 8 log 4 log 2 2 log22 + +xx xBai 26. Giai phng trnh 0 4 2 2 . 4 222 2 + + x x x x xBai 27. Giai phng trnh 4x 2x+1 +2(2x -1)sin(2x+y-1) + 2 = 0Bai 28. Giai phng trnh :6 ) 3 3 ( log ). 1 3 ( log13 3 + x xBai 29. Ghpt: ' + + +0 2 0 1 2) 1 l n ( ) 1 l n (2 2y x y xy x y xBai 30. Giai phng trnh : 041log log ). 1 log ( 22 4 2 + + x xBai 31. Gbpt:) 1 2 ( log 1 2 log 4 ) 144 4 ( log25 5 5+ + < + x xBai 32. Giai phng trnh : 0 ) 1 ( log ) 3 ( log 1 log38212 + x x xBai 33. Giai phng trnh 0 1 3 . 10 92 12 2 + + + x x x xTrang 34Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Bai 34. CSPA-04Ghpt' + +4 l o g l o g 25 ) ( l o g2 42 22y xy xBai 35. Giai bat phng trnh5 2 4 2 81 1> + ++ + x x xBai 36. Giai 32x+4 + 45.6x 9.22x+20Bai 37. CKT-05Tm tap xac nh cua ham so) 2 5 ( log25+ x x yBai 38. Tm m e phng trnh x3 -3x + 2m 6 = 0 co ba nghiem phan biet.Bai 39. CSP-05Ghpt: ' + 1 ) 3 ( l o g ) 3 ( l o g5 95 52 2y x y xy xBai 40. Gbpt: 24 5 52 21 1> + x xBai 41. Tm m e ham so:4 cos 2 cos lg + + x m x y xac nhR x Bai 42. CY-05Gbpt:) log 4 .( 2 log . 4 log416 225 , 0x x x +Bai 43. CCN2-06 Giai phng trnh 0 4 4 . 2 42 22 2 + + x x x xBai 44.Giai phng trnh 34x -4.32x + 3 = 0Bai 45. HTDTT N06Cho bat phn g trnh a.4x +(a-1).2x+2 + a -1 = 0a) Giai bat phng trnh khi a = 65b) Tm a e bat phng trnh ung vi moi x thuoc R. Bai 46. Giai phng trnh 1 + log2(9x 6) = log2(4.3x 6)Bai 47. CTCKT 06 Giai bat phng trnh 0 2 log log . 32421> + x xBai 48. Giai phng trnh log9(x+8) log3(x+26) + 2 = 0Bai 49. Giai he ' 1 2 2 . 62 3 . 2 6y xy xBai 50. Giai phng trnh 1 2 . 32x xBai 51. Giai phng trnh 125x + 50x = 23x+1Bai 52. Giai phng trnh 1 ) 7 ( log ) 1 ( log ) 1 ( log212121 + + x x xBai 53. Giai phng trnh8x + 18x =2.27xBai 54. CSP-06 Gbpt:2 ) 2 2 ( log ). 1 2 ( log12 2> + x xBai 55. Giai phng trnh 0 4 . 6 6 . 13 9 . 61 cos cos 2 1 cos cos 2 1 cos cos 22 2 2 + + + + x x x x x xBai 56. Gbpt: 0 6 log ) 1 ( log 2 log24121 + + x xBai 57. Gbpt: ( ) [ ] 0 2 log log224< + x x xBai 58. Giai bat phng trnh 4216 4 21> +xxxTrang 35Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Bai 59.Giai he' + + +y xx y y xx y x 12 22 2Bai 60. Giai bat phng trnh 3 )31.( 2 92 22 2 x x x xBai 61. D-08 Gii bt phng trnh212x 3x 2log 0x +MT S PHNG TRNH M LGA SIU VITTrang 36Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 362 23 2 /2log ( 1)2 3log 2 22 6 25log log 5 21)2 8 142)1 8 33)log (1 ) log4)25)log ( 3 ) log 6)log ( 2 3) log ( 2 4)7) 3 x x xxxxx xx x xx x x x x xx x+ + ++ + + [ ]2log22 2 2 2x2 3 2 x8) 2.3 =39)log ( -4) log 8(x+2)10)log 3log (3 1) 111)3 4 0 12)3 4 513)3 (3 10).3 3 014)3.4 (3 10)xx x xx xxx x x xxx x x + 1 + ]+ + + + +2 22 x2 2x 6 10 21.2 3 015)log log 1 1 16)4.9 12 3. 16 017)3 os2x 18)3 6 619)9 2( 2).3 2 5 020)4 -4 3.2 21)(4 15)xx xx xx x x x x xxxx xc x xx x ++ +++ + + + + + +22os2x oslg lg62(4- 15) 62 22)4 4 323)6 1224 )6 8 101 125)log 8log 2 326) lg( 2)2 827) 4 6 9 x c c xx x x xx xx x xxx x+ + + + ++ 522lg lg5 lg 237 3 3 2log ( 3) 28)( 1 1 2)log ( ) 029)5 5030) 100031)log log ( 2) 32)3log (1 ) 2log33)234x xxx x x xx x xx x x x xx++ + + ++ 32 72412 9) log (1 ) log135)log ( ) log36)lg( 6) lg( 2) 42x xx x x x x x x+ + + +h ph ng trnh m v h ph ng trnh logarit Gii cc h phng trnh:1) ( ) ( )2 2log 5 logl g l g41l g l g3x y x yo x oo y o + ' 2) ( ) ( )3 34 32log 1 logx yy xx y x y+' + 3) '+ 511 0 5 1 52xyyx x4) ( )' ++3 2 3 l o g2 l o g1yyxx5) ( )( )' + +y xx yy xy x226 91 2226) ' 1 2331 l o gyxx y7) ( )2 449 27.3 01 1l g l g lg 44 2xy yo x o y x '+ Trang 37Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 8) ( )' +2 l o g1 1 5 2 2 . 35y xy x9) ( )( ) ( )2 2l g 1 l g8l g l g l g3o x y oo x y o x y o + +'+ 10) ( )' 2 l o g9 7 2 2 . 33y xy x11) ( )( ) ( ) ( )'+ +x y x y x yx y5 5 5l o g 2 1l o g l o g 1 2 2 l o g 24 8 3312)( ) ( ) ( ) y x y x y x + +32 233 39log log log13) ( )' + +0 2 0 21 l o g 2 l o g l o g1 8a y xa y xa a14) ( )( )' + +y x y xy xx y5l o g 32 75315) ( ) ( )'+++ + 85 35 4 21 2y xy xy xy xx y x y16) ( ) ( )'> 0 x 6 4 222yyxx17) ' + +315 21 21l o gl o g2252y xxyyx18) ( )'> ++ 0 x 811 0 72y xxy y19) ' +

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3 20 5 l o g 2 l o g 2212x yy xxy20) ( ) ( )1l g 3 l g 5 04 4 8 8 0yx y xo x o y ' 21) ( )( )' + +2 3 2 l o g2 2 3 l o gy xy xyx29) '

,_

+5 l o g l o g 2 21 212y xy xxy30) ( )'> 0 x 211 62 2y xxy x31) ( )' +2 l g l g l g1 l g2x yy x32) ' 32 2 . 7 432x yyyxxTrang 38Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 33) ' +6 8 9 2 52 0 0 2 . 52 233y xy x34) ( )2 21l g 1,522210 100 1010 632 10 9o x yx yx y+ +'+ + 22) ( )'> + +0 y 6 45 , 15 , 2 xx xyy y23) ( )( ) ( )l g l g5 l g l g l g6l g1l g 6 l g l g6o x y o o x o y oo xo y o y o+ + ' + +24) ( )' 1 l o g1 l o g l o g22x yxxyy x y25) ( ) ( )' +1 l o g l o g2 2y xy x y xy x26) ( )' + 9 l o g 2 43 662x y xxy x27) ( ) ( )' +21 l o g l o g2 22 2v uv u v u28) ( )' 0 p q v q pyxyxy xaaaq pl o gl o gl o g35) ( ) ( )l g l gl g4 l g33 44 3o x o yo ox y '36)( )'< +0 a2 2 2 22l g 5 , 2 l g l g a y xa xy37) ' +1 l o g l o g44 4l o g l o g8 8y xy xx y38 ) ( )( )' + +1 3 7 , 01 21 6 2822x xy xy xxy xy x39) ' +1 l o g l o g2 7 23 3l o g l o g3 3x yy xx y40) ' ++4 25 2 2y xy x41) 'yyxx5 21 0 8 42) ' + 0 4 50 l o g l o g 5 , 02 22 2y xy xTrang 39Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 43) '1 62l o gl o gyxxyyx44) ' + + +2 285 1 2l o g l o gl o g l o gl o g l o gz xy xz zx zz zy yy zx yz x45) ( )' + ++ +1 1222x xyy x46) ' +129 9y xy xy x y x47) '1 8 2 . 31 2 3 . 2y xy x48) ( )( ) ( )' + + + 1 1 12 3 92 23 l o g l o g2 2y xx yx y49) 2cot sinsin cot9 39 81 2x yy gx+ ' 50) ' +2 2 21y xy x51) '+ + + ++ +1 1 32 . 3 2 223 2 1 3x x y xx y y x52) ( )' 1 2 l o g . l o g35 , 2l o gx y yx y xyxyCAU HOI TRAC NGHIEMLu thaCu1: Tnh: K = 40,7531 116 8 _ _+ , ,, ta c:A. 12B. 16C. 18D. 24Cu2: Tnh: K = ( )3 1 3 403 22.2 5 .510 :10 0,25 +, ta c A. 10 B. -10 C. 12D. 15Cu3: Tnh: K = ( )( )332 2303 212: 4 3915 .25 0,7 .2 _+ , _+ ,, ta cA. 3313B. 83C. 53D. 23Cu4: Tnh: K = ( ) ( )21,530,04 0,125 , ta cA. 90B. 121 C. 120 D. 125Trang 40Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu5: Tnh: K = 9 2 6 47 7 5 58 :8 3 .3 , ta cA. 2 B. 3 C. -1D. 4Cu6: Cho a l mt s dng, biu thc 23a a vit di dng lu tha vi s m hu t l:A. 76aB. 56a C. 65a D. 116aCu7: Biu thc a43 23: avit di dng lu tha vi s m hu t l:A. 53a B. 23aC. 58a D. 73aCu8: Biu thc 6 5 3x. x. x(x > 0) vit di dng lu tha vi s m hu t l:A. 73x B. 52xC. 23x D. 53xCu9: Cho f(x) = 3 6x. x. Khi f(0,09) bng:A. 0,1B. 0,2 C. 0,3 D. 0,4Cu10: Cho f(x) = 3 26x xx. Khi f1310 _ , bng:A. 1B. 1110 C. 1310 D. 4Cu11: Cho f(x) = 12 5 3 4x x x. Khi f(2,7) bng:A. 2,7 B. 3,7 C. 4,7 D. 5,7Cu12: Tnh: K = 3 2 1 2 4 24 .2 :2+ +, ta c:A. 5B. 6 C. 7 D. 8Cu13: Trong cc phng trnh sau y, phng trnh no c nghim?A. 16x + 1 = 0 B. x 4 5 0 + C. ( )1156x x 1 0 + D. 14x 1 0 Cu14: Mnh no sau y l ng?A. ( ) ( )43 2 3 25 < B. ( ) ( )611 2 11 27 > C. ( ) ( )3 42 2 2 2 < D. ( ) ( )3 44 2 4 2 < Cu15: Chn mnh ng trong cc mnh sau:A. 3 24 4 >B. 3 1,73 3 . Kt lun no sau y l ng?A. < B. > C. + = 0 D. .= 1Cu17: Cho K = 1 21 12 2y yx y 1 2x x _ _ + , ,. biu thc rt gn ca K l:A. x B. 2x C. x + 1 D. x - 1Cu18: Rt gn biu thc: 4 281a b, ta c:A. 9a2b B. -9a2b C. 29a bD. Kt qu khc Cu19: Rt gn biu thc: ( )484x x 1 + , ta c:A. x4(x + 1) B. 2x x 1 +C. - ( )24x x 1 + D.( ) x x 1 +Cu20: Rt gn biu thc: x x x x: 1116x, ta c:A. 4xB. 6xC. 8xD. xTrang 41Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu21: Biu thc K = 3 32 2 23 3 3 vit di dng lu tha vi s m hu t l:A. 51823 _ ,B. 11223 _ ,C. 1823 _ ,D. 1623 _ ,Cu22: Rt gn biu thc K = ( ) ( ) ( )4 4x x 1 x x 1 x x 1 + + + + ta c:A. x2 + 1 B. x2 + x + 1C. x2 - x + 1 D. x2 - 1Cu23: Nu ( )1a a 12 + th gi tr ca l:A. 3B. 2 C. 1 D. 0Cu24: Cho 3 27 3 C. < 3 D. RCu25: Trc cn thc mu biu thc 3 315 2 ta c:A. 3 3 325 10 43+ +B. 3 35 2 +C. 3 3 375 15 4 + +D. 3 35 4 +Cu26: Rt gn biu thc 2 121aa _ , (a > 0), ta c:A. a B. 2a C. 3a D. 4aCu27: Rt gn biu thc ( )23 12 3b : b(b > 0), ta c:A. b B. b2C. b3D. b4Cu28: Rt gn biu thc 4 2 4x x : x (x > 0), ta c:A. 4xB. 3xC. xD. 2xCu29: Cho x x9 9 23+ . Khi o biu thc K = x xx x5 3 31 3 3+ + c gi tr bng:A. 52 B. 12C. 32D. 2Cu30: Cho biu thc A =( ) ( )1 1a 1 b 1 + + + . Nu a = ( )12 3+v b = ( )12 3th gi tr ca A l:A. 1 B. 2 C. 3 D. 4Hm s Lu thaCu1: Hm s y = 3 21 x c tp xc nh l:A. [-1; 1] B. (-; -1] [1; +) C. R\{-1; 1} D. RCu2: Hm s y = ( )424x 1c tp xc nh l:A. R B. (0; +)) C. R\1 1;2 2 ' ) D. 1 1;2 2 _ ,Cu3: Hm s y = ( )3254 x c tp xc nh l:A. [-2; 2] B. (-: 2] [2; +) C. R D. R\{-1; 1}Cu4: Hm s y = ( )e2x x 1+ c tp xc nh l:A. R B. (1; +) C. (-1; 1) D. R\{-1; 1}Trang 42Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu5: Hm s y = ( )223x 1 +c o hm l:A. y = 3 24x3 x 1 +B. y = ( )2234x3 x 1 +C. y = 3 22x x 1 +D. y = ( )2234x x 1 +Cu6: Hm s y = 3 22x x 1 + c o hm f(0) l:A. 13 B. 13C. 2 D. 4Cu7: Cho hm s y = 4 22x x . o hm f(x) c tp xc nh l:A. R B. (0; 2) C. (-;0) (2; +) D. R\{0; 2}Cu8: Hm s y = 3 3a bx + c o hm l:A. y = 3 3bx3 a bx +B. y = ( )2233bxa bx +C. y = 3 2 33bx a bx +D. y = 23 33bx2 a bx +Cu9: Cho f(x) = 3 2 2x x. o hm f(1) bng:A. 38B. 83C. 2 D. 4Cu10: Cho f(x) = 3x 2x 1+. o hm f(0) bng:A. 1 B. 314C. 32D. 4Cu11:Trong cc hm s sau y, hm s no ng bin trn cc khong n xc nh?A. y = x-4B. y=34xC. y = x4D. y = 3xCu12: Cho hm s y =( )2x 2+ . H thc gia y v y khng ph thuc vo x l:A. y + 2y = 0 B. y- 6y2 = 0 C. 2y - 3y = 0 D. (y)2 - 4y = 0Cu13: Cho hm s y = x-4. Tm mnh sai trong cc mnh sau:A. th hm s c mt trc i xng.B. th hm s i qua im (1; 1)C. th hm s c hai ng tim cnD. th hm s c mt tm i xng Cu14:Trn th (C) ca hm s y = 2xly im M0c honh x0= 1. Tip tuyn ca (C) ti im M0 c phng trnh l:A. y =x 12+ B. y =x 12 2 + C. y=x 1 + D. y =x 12 2 + +Cu15:Trn th ca hm s y = 12x+ly im M0c honh x0= 22. Tip tuyn ca (C) ti im M0 c h s gc bng:A. + 2 B. 2 C. 2- 1 D. 3LgartCu1: Cho a > 0 v a 1. Tm mnh ng trong cc mnh sau: A. alog x c ngha vi xB. loga1 = a v logaa = 0C. logaxy = logax.logay D. na alog x nlog x (x > 0,n 0)Cu2:Cho a > 0 v a 1, x v y l hai s dng. Tm mnh ng trong cc mnh sau: Trang 43Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton A. aaalog x xlogy log yB. aa1 1logx log xC.( )a a alog x y log x log y + +D. b b alog x log a.log x Cu3: 44log 8 bng:A. 12B. 38C. 54D. 2Cu4: 3 71alog a (a > 0, a 1) bng:A. -73B. 23C. 53D. 4Cu5: 418log 32 bng:A. 54B. 45C. -512D. 3Cu6: 0,5log 0,125 bng:A. 4 B. 3 C. 2 D. 5Cu7: 3 5 2 2 4a15 7a a aloga _ , bng:A. 3 B. 125C. 95D. 2Cu8: 7log 249bng:A. 2 B. 3 C. 4 D. 5Cu9: 21log 10264 bng:A. 200 B. 400 C. 1000 D. 1200Cu10: 2 2lg710+ bng:A. 4900 B. 4200 C. 4000 D. 3800Cu11: 2 81log 3 3log 524+ bng:A. 25 B. 45 C. 50 D. 75Cu12: a3 2log ba (a > 0, a 1, b > 0) bng:A. 3 2a bB. 3a bC. 2 3a bD. 2abCu13: Nu xlog 243 5 th x bng:A. 2 B. 3 C. 4 D. 5Cu14: Nu 3xlog 2 2 4 th x bng:A. 312B. 32C. 4 D. 5Cu15: ( )2 4 123log log 16 log 2 + bng:A. 2 B. 3 C. 4 D. 5Cu16: Nu a a a a1log x log 9 log 5 log 22 +(a > 0, a 1) th x bng:A. 25B. 35C. 65D. 3Cu17: Nu a a a1log x (log 9 3log 4)2 (a > 0, a 1) th x bng:Trang 44Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton A. 2 2B. 2C. 8 D. 16Cu18: Nu 2 2 2log x 5log a 4log b + (a, b > 0) th x bng:A. 5 4a bB. 4 5a bC. 5a + 4b D. 4a + 5bCu19: Nu 2 37 7 7log x 8log ab 2log a b (a, b > 0) th x bng:A. 4 6a bB. 2 14a bC. 6 12a bD. 8 14a bCu20: Cho lg2 = a. Tnh lg25 theo a?A. 2 + a B. 2(2 + 3a) C. 2(1 - a) D. 3(5 - 2a)Cu21: Cho lg5 = a. Tnh 1lg64 theo a?A. 2 + 5a B. 1 - 6a C. 4 - 3a D. 6(a - 1)Cu22: Cho lg2 = a. Tnh lg1254theo a?A. 3 - 5a B. 2(a + 5) C. 4(1 + a) D. 6 + 7aCu23: Cho 2log 5 a . Khi 4log 500tnh theo a l:A. 3a + 2 B.( )13a 22+ C. 2(5a + 4) D. 6a - 2Cu24: Cho 2log 6 a . Khi log318 tnh theo a l:A. 2a 1a 1B. aa 1 +C. 2a + 3 D. 2 - 3aCu25: Cho log2 35 a; log 5 b . Khi 6log 5 tnh theo a v b l:A. 1a b +B. aba b +C. a + b D. 2 2a b +Cu26: Gi s ta c h thc a2 + b2 = 7ab (a, b > 0). H thc no sau y l ng?A.( )2 2 22log a b log a log b + +B. 2 2 2a b2log log a log b3+ +C.( )2 2 2a blog 2 log a log b3+ + D. 42 2 2a blog log a log b6+ +Cu27: 43log 8.log 81 bng:A. 8 B. 9 C. 7 D. 12Cu28: Vi gi tr no ca x th biu thc( )26log 2x x c ngha?A. 0 < x < 2 B. x > 2 C. -1 < x < 1 D. x < 3Cu29: Tp hp cc gi tr ca x biu thc( )3 25log x x 2x c ngha l:A. (0; 1) B. (1; +) C. (-1; 0) (2; +) D. (0; 2) (4; +)Cu30: 36log 3.log 36 bng:A. 4 B. 3 C. 2 D. 1Hm s m - hm s lgartCu1: Tm mnh ng trong cc mnh sau:A. Hm s y = ax vi 0 < a < 1 l mt hm s ng bin trn (-: +)B. Hm s y = ax vi a > 1 l mt hm s nghch bin trn (-: +)C. th hm s y = ax (0 < a 1) lun i qua im (a ; 1)D. th cc hm s y = ax v y = x1a _ , (0 < a 1) th i xng vi nhau qua trc tungCu2: Cho a > 1. Tm mnh sai trong cc mnh sau: A. ax > 1 khi x > 0Trang 45Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton B. 0 < ax < 1 khi x < 0C. Nu x1 < x2 th 1 2x xa a 1 khi x < 0B. 0 < ax < 1 khi x > 0C. Nu x1 < x2 th 1 2x xa a 1 l mt hm s nghch bin trn khong (0 ; +)C. Hm s y = alog x (0 < a 1) c tp xc nh l R D. th cc hm s y = alog x v y = 1alog x (0 < a 1) th i xng vi nhau qua trc honhCu5: Cho a > 1. Tm mnh sai trong cc mnh sau:A. alog x > 0 khi x > 1B. alog x< 0 khi 0 < x < 1C. Nu x1 < x2 th a 1 a 2log x log x 0 khi 0 < x < 1B. alog x< 0 khi x > 1C. Nu x1 < x2 th a 1 a 2log x log x 0, a 1. Tm mnh ng trong cc mnh sau: A. Tp gi tr ca hm s y = ax l tp RB. Tp gi tr ca hm s y = alog x l tp RC. Tp xc nh ca hm s y = ax l khong (0; +)D. Tp xc nh ca hm s y = alog x l tp RCu8: Hm s y =( )2ln x 5x 6 + c tp xc nh l:A. (0; +) B. (-; 0) C. (2; 3) D. (-; 2) (3; +)Cu9: Hm s y = ( )2ln x x 2 x + c tp xc nh l:A. (-; -2) B. (1; +) C. (-; -2) (2; +) D. (-2; 2)Cu10: Hm s y = ln1 sinx c tp xc nh l:A. R \ k2 , k Z2 + ' ) B.{ } R \ k2 , k Z + C. R \ k , k Z3 + ' ) D. RCu11: Hm s y = 11 lnx c tp xc nh l:A. (0; +)\ {e} B. (0; +) C. R D. (0; e)Cu12: Hm s y =( )25log 4x x c tp xc nh l:A. (2; 6) B. (0; 4) C. (0; +) D. RCu13: Hm s y = 51log6 x c tp xc nh l:A. (6; +) B. (0; +) C. (-; 6) D. RTrang 46Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu14: Hm s no di y ng bin trn tp xc nh ca n?A. y =( )x0,5 B. y = x23 _ ,C. y = ( )x2 D. y = xe _ ,Cu15: Hm s no di y th nghch bin trn tp xc nh ca n?A. y = 2log xB. y = 3log xC. y = elog xD. y = log xCu16: S no di y nh hn 1?A. 223 _ ,B. ( )e3 C. e D. eCu17: S no di y th nh hn 1?A.( ) log 0,7B. 3log 5C. 3log eD. elog 9Cu18: Hm s y =( )2 xx 2x 2 e + c o hm l:A. y = x2exB. y = -2xexC. y = (2x - 2)exD. Kt qu khc Cu19: Cho f(x) = x2ex. o hm f(1) bng :A. e2B. -e C. 4e D. 6eCu20: Cho f(x) = x xe e2. o hm f(0) bng:A. 4 B. 3 C. 2 D. 1Cu21: Cho f(x) = ln2x. o hm f(e) bng:A. 1eB. 2eC. 3eD. 4eCu22: Hm s f(x) = 1 lnxx x+c o hm l:A. 2lnxx B. lnxxC. 4lnxxD. Kt qu khc Cu23: Cho f(x) =( )4ln x 1 +. o hm f(1) bng:A. 1 B. 2 C. 3 D. 4Cu24: Cho f(x) = lnsin2x. o hm f8 _ , bng:A. 1 B. 2 C. 3 D. 4Cu25: Cho f(x) = lntanx. o hm f '4 _ , bng:A. 1 B. 2 C. 3 D. 4Cu26: Cho y = 1ln1 x +. H thc gia y v y khng ph thuc vo x l:A. y - 2y = 1 B. y + ey = 0 C. yy - 2 = 0 D. y - 4ey = 0Cu27: Cho f(x) = sin2xe. o hm f(0) bng:A. 1 B. 2 C. 3 D. 4Cu28: Cho f(x) = 2cos xe. o hm f(0) bng:A. 0 B. 1 C. 2 D. 3Cu29: Cho f(x) = x 1x 12+. o hm f(0) bng:A. 2 B. ln2 C. 2ln2 D. Kt qu khc Trang 47Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu30: Cho f(x) = tanx v (x) = ln(x - 1). Tnh ( )( )f ' 0' 0 . p s ca bi ton l:A. -1 B.1C. 2 D. -2Cu31: Hm s f(x) = ( )2ln x x 1 + + c o hm f(0) l:A. 0 B. 1 C. 2 D. 3Cu32: Cho f(x) = 2x.3x. o hm f(0) bng:A. ln6 B. ln2 C. ln3 D. ln5Cu33: Cho f(x) = xx . . o hm f(1) bng:A. (1 + ln2) B. (1 + ln ) C. ln D. 2lnCu34: Hm s y = cosx sinxlncosx sinx+ c o hm bng:A. 2cos2xB. 2sin2xC. cos2x D. sin2xCu35: Cho f(x) =( )22log x 1 +. o hm f(1) bng:A. 1ln2B. 1 + ln2 C. 2 D. 4ln2Cu36: Cho f(x) = 2lg x. o hm f(10) bng:A. ln10 B. 15ln10C. 10 D. 2 + ln10Cu37: Cho f(x) = 2xe. o hm cp hai f(0) bng:A. 1 B. 2 C. 3 D. 4Cu38: Cho f(x) = 2x lnx. o hm cp hai f(e) bng:A. 2 B. 3 C. 4 D. 5Cu39: Hm s f(x) = xxe t cc tr ti im:A. x = e B. x = e2C. x = 1 D. x = 2Cu40: Hm s f(x) = 2x lnx t cc tr ti im:A. x = e B. x = eC. x = 1eD. x = 1eCu41: Hm s y = axe (a 0) c o hm cp n l:A. ( ) n axy e B. ( ) n n axy a e C. ( ) n axy n!e D. ( ) n axy n.e Cu42: Hm s y = lnx c o hm cp n l:A. ( ) nnn!yx B. ( )( )( ) n 1nnn 1 !y 1x+ C. ( ) nn1yx D. ( ) nn 1n!yx+Cu43: Cho f(x) = x2e-x. bt phng trnh f(x) 0 c tp nghim l:A. (2; +) B. [0; 2] C. (-2; 4] D. Kt qu khc Cu44: Cho hm s y = sinxe. Biu thc rt gn ca K = ycosx - yinx - y l:A. cosx.esinxB. 2esinxC. 0 D. 1Cu45: th (L) ca hm s f(x) = lnx ct trc honh ti im A, tip tuyn ca (L) ti A c phng trnh l:A. y = x - 1 B. y = 2x + 1 C. y = 3x D. y = 4x - 3Ph ng trnh m v ph ng trnh lgart Cu1: Phng trnh 3x 24 16 c nghim l:A. x = 34B. x = 43C. 3 D. 5Trang 48Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Cu2: Tp nghim ca phng trnh: 2x x 41216 l:A.B. {2; 4} C. { } 0; 1D. { } 2; 2 Cu3: Phng trnh 2x 3 4 x4 8+ c nghim l:A. 67B. 23C. 45D. 2Cu4: Phng trnh x2x 320,125.48 _

, c nghim l:A. 3 B. 4 C. 5 D. 6Cu5: Phng trnh: x x 1 x 2 x x 1 x 22 2 2 3 3 3 + + + c nghim l:A. 2 B. 3 C. 4 D. 5Cu6: Phng trnh: 2x 6 x 72 2 17+ ++ c nghim l:A. -3 B. 2 C. 3 D. 5Cu7: Tp nghim ca phng trnh: x 1 3 x5 5 26 + l:A. { } 2; 4B. { } 3; 5C. { } 1; 3D. Cu8: Phng trnh: x x x3 4 5 + c nghim l:A. 1 B. 2 C. 3 D. 4Cu9: Phng trnh: x x x9 6 2.4 + c nghim l: A. 3 B. 2 C. 1 D. 0Cu10: Phng trnh: x2 x 6 + c nghim l:A. 1 B. 2 C. 3 D. 4Cu11: Xc nh m phng trnh: x x4 2m.2 m 2 0 + + c hai nghim phn bit? p n l:A. m < 2 B. -2 < m < 2 C. m > 2 D. m Cu12: Phng trnh:( ) + l ogx l og x 9 1 c nghim l:A. 7 B. 8 C. 9 D. 10Cu13: Phng trnh:( )3lg 54 x = 3lgx c nghim l:A. 1 B. 2 C. 3 D. 4Cu14: Phng trnh:( ) lnx ln 3x 2 + = 0 c my nghim?A. 0 B. 1 C. 2 D. 3Cu15: Phng trnh:( ) ( ) ( ) ln x 1 ln x 3 ln x 7 + + + +A. 0 B. 1 C. 2 D. 3Cu16: Phng trnh: 2 4 8log x log x log x 11 + + c nghim l:A. 24 B. 36 C. 45 D. 64Cu17: Phng trnh: 2 xlog x 3log 2 4 + c tp nghim l:A. { } 2; 8B. { } 4; 3C. { } 4; 16D. Cu18: Phng trnh:( ) ( )2lg x 6x 7 lg x 3 + c tp nghim l:A. { } 5B. { } 3; 4C. { } 4; 8D. Cu19: Phng trnh: 1 24 lgx 2 lgx+ + = 1 c tp nghim l:A. { } 10; 100B. { } 1; 20C. 1; 1010 ' ) D. Cu20: Phng trnh: +2 logxx 1000 c tp nghim l:Trang 49Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton A. { } 10; 100B. { } 10; 20C. 1; 100010 ' ) D. Cu21: Phng trnh: 2 4log x log x 3 + c tp nghim l:A. { } 4B. { } 3C. { } 2; 5D. Cu22: Phng trnh: 2log x x 6 + c tp nghim l:A. { } 3B. { } 4C. { } 2; 5D. H ph ng trnh m v lgart Cu1: H phng trnh: x yx y2 2 62 8+ + ' vi x y c my nghim?A. 1 B. 2 C. 3 D. 0Cu2: H phng trnh: y 1 xx y3 2 54 6.3 2 0+ ' + c nghim l:A.( ) 3; 4B.( ) 1; 3C.( ) 2; 1D.( ) 4; 4Cu3: H phng trnh: 2x yx 2y 14 16++ ' c my nghim?A. 0 B. 1 C. 2 D. 3Cu4: H phng trnh:1yx22x y 42 .4 64++ ' c nghim l:A.( ) 2; 1B.( ) 4; 3 C.( ) 1; 2D.( ) 5; 5 Cu5: H phng trnh: x y 7lgx lgy 1+ '+ vi x y c nghim l?A.( ) 4; 3B.( ) 6; 1C.( ) 5; 2D. Kt qu khc Cu6: H phng trnh: lgxy 5lgx.lgy 6 ' vi x y c nghim l?A.( ) 100; 10B.( ) 500; 4C.( ) 1000; 100D. Kt qu khcCu7: H phng trnh: 2 22 2x y 20log x log y 3 + '+ vi x y c nghim l:A.( ) 3; 2B.( ) 4; 2C. ( )3 2; 2D. Kt qu khcCu8: H phng trnh: x y2 22 .4 64log x log y 2 '+ c nghim l:A.( ) ( ) 4; 4 , 1; 8B.( ) ( ) 2; 4 , 32; 64C.( ) ( ) 4; 16 , 8; 16D.( ) ( ) 4; 1 , 2; 2Cu9: H phng trnh: x y 6lnx lny 3ln6 '+ c nghim l:A.( ) 20; 14B.( ) 12; 6C.( ) 8; 2D.( ) 18; 12Cu10: H phng trnh: 3lgx 2lgy 54lgx 3lgy 18 '+ c nghim lA.( ) 100; 1000B.( ) 1000; 100C.( ) 50; 40D. Kt qu khcTrang 50Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Bt phng trnh m v lgartCu1: Tp nghim ca bt phng trnh: 14x 11 12 2 _ _< , , l:A.( ) 0; 1B. 51;4 _ ,C.( ) 2;+D.( ) ;0 Cu2: Bt phng trnh: ( ) ( )2x 2x 32 2 c tp nghim l:A.( ) 2;5 B. [ ] 2;1 C. [ ] 1;3 D. Kt qu khc Cu3: Bt phng trnh: 2 x x3 34 4 _ _ , , c tp nghim l:A. [ ] 1; 2 B. [ ] ; 2 C. (0; 1) D. Cu4: Bt phng trnh: x x 14 2 3+< + c tp nghim l:A.( ) 1; 3 B.( ) 2; 4 C.( )2log 3; 5D.( )2;log 3 Cu5: Bt phng trnh: x x9 3 6 0 3x c tp nghim l:A. ( ) ;0 B.( ) 1;+ C.( ) 0;1 D.( ) 1;1 Cu7: H bt phng trnh: x 1 6 2x4x 5 1 x4 83 27+ + + ' c tp nghim l:A. [2; +) B. [-2; 2] C. (-; 1] D. [2; 5]Cu8: Bt phng trnh: ( ) ( )2 2log 3x 2 log 6 5x > c tp nghim l:A. (0; +) B. 61;5 _ ,C. 1;32 _ ,D. ( ) 3;1 Cu9: Bt phng trnh: ( ) ( )4 2log x 7 log x 1 + > +c tp nghim l:A.( ) 1;4 B.( ) 5;+ C. (-1; 2) D. (-; 1)Cu10: gii bt phng trnh: ln2xx 1 > 0 (*), mt hc sinh lp lun qua ba bc nh sau:Bc1: iu kin: 2x0x 1> x 0x 1<

>(1)Bc2: Ta c ln2xx 1 > 0 ln2xx 1 > ln1 2x1x 1> (2)Bc3: (2) 2x > x - 1 x > -1 (3)Kt hp (3) v (1) ta c 1 x 0x 1 < <

>Vy tp nghim ca bt phng trnh l: (-1; 0) (1; +)Hi lp lun trn ng hay sai? Nu sai th sai t bc no?A. Lp lun hon ton ng B. Sai t bc 1 C. Sai t bc 2 D. Sai t bc 3Cu11: H bt phng trnh: ( ) ( )( ) ( )2 20,5 0,5log 2x 4 log x 1log 3x 2 log 2x 2 +' + c tp nghim l:A. [4; 5] B. [2; 4] C. (4; +) D. Trang 51Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton GIAI PHNG TRNH49/Gii cc phng trnh sau:a.( )2 2 2 2 2x 3x 2 x 6x 5 2 2x 3x 7 x 3x 2 2x 3x 744 4 x 6x 5 log 4 4 1 4 1. + + + + + ++ + + + +S: x 1; 5; 2. t b.( )( )3log 2x 12 3log x x log 2x 1 2+ + S:x=1;250/Gii cc phng trnh sau:a.( )3log x3 7log x 3x 2 log 3x 2 7 + S:x=1;2b.x 1x 13x 3x3 4 3 4 21. . .4 3 4 3 16 _ _+ , , S:V nghim51/Gii cc phng trnh sau:a.( )( )22log 7x 62 22log x x 2log 7x 6 4+ +S:x=1;2b.( )x xx 5 25 49x x 2(5 24) x2(5 24) 5 7 5 5 7 25 .+ ++ + + + S: x = 2.52/Gii cc phng trnh sau:a.( )( )( )3log 2x 125 32log x 5 log 2x 1 x S:x=1;2b.( )x xx x 4 37 4 5 4 327 3 .+ 11 1 ] S: x = 10. 53/Gii cc phng trnh sau:a.( ) ( )x 1xx5 5x 15.8 x 3. log 2 503 2log 2x+ + + S:5x 3; log 2. b. ( ) ( ) ( ) ( ) ( ) ( ) ( )6 7 2 5 2 7 6 58log x.log x log 3x 2 .log 4x 3 2 log 3x 2 .log x 2.log x. log 4x 3 + + S:x=1;254/Gii cc phng trnh sau:a. ( ) ( )x 1 x x5 5xx 3. log 2 5. 8 102 2log 2x 1++ + ++S: 5x 2; 1 log 2. b.( )( )( )6log 5x 422 62log x x 8 3log 5x 4+ S:x=1;255/Gii cc phng trnh sau:a.( )xx x25x3 4 5 log 3 42 S: x = 2.b.( )3log x 23 17log x 4x 4x 1 2log 2x 1 17 + S:x=1;2Trang 52Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton 56/Gii cc phng trnh sau:a.( )7log x7 37log x 6x log 6x 5 37 5 + S:x=1;2b.( )x x x x x4(2 3) (2 3) x 4 log (2 3) (2 3) + + + + S: x = 1.57/Gii cc phng trnh sau:a.x x xx x ( 3 2) x ( 5) ( 3 2)( 3 2) ( 3 2) 3 ( 5) 3+ + + + +S: Vo nghiemb.( )( ) ( )7log x7 1313 log x 2x 1 log 2x 1 + + S:x=1;258/Gii cc phng trnh sau:a. ( ) ( )5log (x 3)2 52 log x x log x 3+ + S: x = 2.b.( )( )( )x2x25 5 13 13log x log x log 4x 4x 1 log 2x 1 + S:x=1;259/Gii cc phng trnh sau:a.x x 1 x 127 3 x 1 x 1 3x.+ + + + S: x 2.3 tb. ( ) ( ) ( ) ( )11 13 21 37log x log x log 2x 1 log 3x 2 + + S:x=1;260/Gii cc phng trnh sau:a.2 2x 6x 10 2 x 6x 63 2x 12x 16 3 . + + + + S: x = 3.b.( ) ( )( )7log 3x 213 37log x x log 3x 2 3++ + S:x=1;261/Gii cc phng trnh sau:a.( ) ( )3 7log 2x 1 log 3x 22x 2 3 S:x=1;2b.32 xx x3 2.cos 322 x xx x2.cos x 3 3 3 .2 _ , _ + + ,S: x = 0.62/Gii cc phng trnh sau:a.( ) ( )3 2log 2x 1 log 3x 22 4x x 5 6 + +S:x=1;2b.212 2 y 2y 22 2 2 21 1 1log cos xy cos xy 2cos xy cos xy y 2y 2 + _+ + + + + ,S: x K , K z.y 1. '63/Gii cc phng trnh sau:a.( ) ( )37 13log 6x 5 log 2x 12x 7 7 +S:x=1;2b.sin xcosx3 3 sin x cosx + S: x = 0.Trang 53Bi Tp PT&BPT M ,Lgarit Trng THPT Phc Bnh -T Ton Trang 54Trn Minh Hngn tp HK I55