BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
1 Traàn Quang Time goes, you say? Ah, no! Alas, time stays, we go
PHÖÔNG TRÌNH MUÕ
Phương pháp 1: Đưa về cùng cơ số
1. x x x2 3 2 12 16
2.
2 5x 6x
22 16 2
3. 231224 3.23.2 xxxx
4. 2x 4x 1
3243
5. 5 17
7 332 0 25 128, .
x x
x x
6. 3
82
4 35 125
x
x
7. x x 1 x 22 .3 .5 12
8. 2 9 27
3 8 64
x x
9.
21 1
3 22 2 4x
x x
10. 22 5 2 13 27 x x x
11. 1 2 14.9 3 2 x x
12. 3x 1 5x 8(2 3) (2 3)
13. x 1
x 1 x 1( 5 2) ( 5 2)
14. 1331( 10 3) ( 10 3)
xx
xx
15. 31 2 1 32 4 8 2 2 0 125. . . , x x x
16. 3 332 4 0 125 4 2, x x x
17.
2 2
3 9 9
4 16 16
x
x
18. xx x22 1( 1) 1
19. 55 50log log x x
20. 2 3
3 319 27 81
3
x
x x x
21. 2 1 11 13.4 .9 6.4 .9
3 2
x x x x
22. x x 1 x 2 x x 1 x 22 2 2 3 3 3
23. x x 1 x 2 x x 1 x 25 5 5 3 3 3
24. x x 1 x 2 x x 12 2 2 5 5
25. 3 292 22222
xxxxx
26. 2cos1
2cos22 xx
xx
xx
Phương pháp 2: Đặt ẩn phụ.
1. . .2 16 15 4 8 0 x x
2. 9 8.3 7 0 x x
3. 2x 8 x 53 4.3 27 0
4. 2 2
4 6.2 8 0x x
5. 1 3
3
64 2 12 0x x
6. x x2.16 15.4 8 0
7. 2 22 1 24 5.2 6 0x x x x
8. log log525 5 4.x x
9. 2x 6 x 72 2 17 0
10. 2 1 11.4 21 13.4
2
x x
11. 3 2cos 1 cos4 7.4 2 0x x
12. 2 25 1 5
4 12 2 8 0. x x x x
13. 3033 22 xx
14. x 1 3 x5 5 26
15. 2 2
2
2 2 3 x x x x
16. 2 2sin cos9 9 10 x x
17. 82 3loglog2 2 5 0 xxx x
18. 3 1 5 35.2 3.2 7 0x x
19. 1 25 5.0,2 26 x x
20. 14 4 3.2x x x x
21. 2 2sin cos2 5.2 7 x x
22. 2cos2 cos4 4 3x x
23. 15 5 4 0x x
24. 2 2 22 1 2 2 19 34.15 25 0 x x x x x x
25.
1 1 1
x x x2.4 6 9
26. 1 1 1
6.9 13.6 6.4 0x x x
27. 3 3 325 9 15 0x x x
28. 027.21812.48.3 xxxx
29. 07.714.92.2 22 xxx
30. x x x 6.9 13.6 6.4 0
31. 27 12 2.8x x x
32. 2 2 2
15.25 34.15 15.9 0x x x
33. 25 12.2 6,25.0,16 0x x x
34. 1/ 1/ 1/4 6 9x x x
35. 3 1125 50 2 x x x
36. xxx 27.2188
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
2 Traàn Quang Lost time is never found again
37. 2 3 2 3 14x x
38. 2 3 2 3 2 x x
39. 4 15 4 15 8x x
40. x x(2 3) (2 3) 4 0
41. 2 1 2 1 2 2 0x x
42. 02.75353 xxx
43. x x x 3(3 5) 16(3 5) 2
44. x x(7 4 3) 3(2 3) 2 0
45. 26 15 3 2 7 4 3 2 2 3 1x x x
46. cos cos 5
7 4 3 7 4 32
x x
47. 7 3 5 7 3 5 14.2x x
x
48. x x
( 2 3) ( 2 3) 4
49.
x x7 3 5 7 3 5
7 82 2
50. 10245245 xx
51. x x
7 4 3 7 4 3 14
52. 10625625tantan
xx
53. 35 21 7 5 21 2x x
x
54. sin sin
5 2 6 5 2 6 2x x
55.
3
3 1
8 12 6 2 1
2 2
x x
x x
56. 3x x
3(x 1) x
1 122 6.2 1
2 2
57. x x x x2 2 52 2 2 2 20
16
58. 4 4 2 2 10x x x x
59. 1 13 3 9 9 6x x x x
60. 1 3 28 8.0,5 3.2 125 24.0,5x x x x
61. 64)5125.(275.953 xxxx
62. 22 6 2 6x x
63. xxx 9133.4 13
64. 093.613.73.5 1112 xxxx
65. 24223 2212.32.4 xxxx
66. 2 1 1 15.3 7.3 1 6.3 9 0x x x x
67.
2 21 2 1 4
2 3 2 32 3
x x x
Phương pháp 3:
Sử dụng tính đơn điệu của hàm số
1. 4 9 25x x x
2. x x x3 4 5
3. x3 x 4 0
4. xx4115
5. 132 2 x
x
6. x x x3.16 2.8 5.36
7. xxxx 202459
8. 9,2
5
2
2
5/1
xx
9. 2 3 2 3 2x x
x
10. 3 2 3 2 10( ) ( ) x
x x
11. xxx
5.22357
12. xx
6
217.9
13. 3 21 1 15 4 3 2 2 5 7 17
2 3 6x x x x
x x xx x x
14. 2 4 2 23 ( 4)3 1 0x xx
15. 3 .2 3 2 1x xx x
16. 1 1 5
3 5 3 103 4 12
x x x
x x x
17. 1 1 1
3 2 2 63 2 6
x x x
x x x
Phương pháp4:
Đưa về phương trình tích và Đặt ẩn phụ
không toàn phần.
1. 8.3x + 3.2
x = 24 + 6
x
2. 2 1 15 7 175 35 0x x x
3. 0422.42 222
xxxxx
4. 20515.33.12 1 xxx
5. 2 2 23 2 6 5 2 3 7
4 4 4 1 x x x x x x
6. 02.93.9232 xxxx
7. 021.2.232 xx xx
8. 0523.2.29 xx xx
9. 035.10325.3 22 xx xx
10. 1224222 11 xxxx
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
3 Traàn Quang Time goes, you say? Ah, no! Alas, time stays, we go
11. xxx 6132
12. 3 2 3 42 1 2 1.2 2 .2 2x xx xx x
13. 2 23.25 3 10 5 3 0x xx x
14. 9 2 2 .3 2 5 0x xx x
15. 2 3 2 2 1 2 0x xx x
16. 112.3 3.15 5 20x x x
17. 3.4 (3 10)2 3 0x xx x
18. 2 23.16 (3 10)4 3 0x xx x
19. 2 3 1 34 2 2 16 0 x x x
Phương pháp5: Lôgarit hóa
Phương pháp 6:
Hàm đặc trưng và PP đánh giá.
1. 2112212 532532 xxxxxx
2.
2
2 2
1 1 22
2 22
x x
x xx
x
3. 12 4 1x x x
4. 211 1242
xxx
5. xxxxx 3cos.722322 cos.4cos.3
6. 1347321
xxx
7. xx xx 2.1.24 22
8. 123223 1122 xxxxxx
9. xx x
12cos 22
2
10. xx 2cos32
11. x xx2 4 2 24 ( 4)2 1
12. 4 6 25 2x x x
13. 3 5 6 2 x x x
14. x x x 3 2 3 2
PHÖÔNG TRÌNH LOGARIT
Phương pháp 1: Đưa về cùng cơ số
1. 2log (5 1) 4x
2. 3 9 27log log log 11x x x
3. 3 3log log ( 2) 1x x
4. 2
2 2log ( 3) log (6 10) 1 0x x
5. 3 21log( 1) log( 2 1) log
2x x x x
6. 32 2log (1 1) 3log 40 0x x
7. 4 2log ( 3) log ( 7) 2 0x x
8. 2 1
8
log ( 2) 6log 3 5 2x x
9. 3
1 822
log 1 log (3 ) log ( 1)x x x
10. 2 2
1log (4 15.2 27) 2log 0
4.2 3
x x
x
11. 4log ( 2).log 2 1xx
12. 2 2
2 2 2log ( 3 2) log ( 7 12) 3 log 3x x x x
13. 2
9 3 32log log .log ( 2 1 1)x x x
14. 2 3 2 3log log log .logx x x x
15. 5 3 5 9log log log 3.log 225x x
16. 2 3
4 82log ( 1) 2 log 4 log ( 4)x x x
17. 2 2 2
2 3 2 3log ( 1 ) log ( 1 ) 6x x x x
18. 2 2
9 33
1 1log ( 5 6) log log 3
2 2
xx x x
19. 4 2
2 1
1 1log ( 1) log 2
log 4 2x
x x
20. 2
2 2
5log log ( 25) 0
5
xx
x
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
4 Traàn Quang Lost time is never found again
21.
2
6 6
1 11 log log 1
7 2
xx
x
22. 2
3 32log ( 2) log ( 4) 0x x
23.
2log1
log 6 5
x
x
24. 4 4
2log 2 ( 3) log 2
3
xx x
x
25.
2
2 2
log 10 1 log4log2
log (3 2) 2 log 5
x x
x
26.
2log 9 21
3
x
x
27. 2log 1 3log 1 2 log 1x x x
28.
log ( ) log ( )x x
x
1
4 4 2 32 1
2
29.
2
2 1 2
2
1log ( 1) log ( 4) log (3 )
2x x x
30. 2 2
1log (4 15.2 27) 2log 0
4.2 3
x x
x
31. 8
4 22
1 1log ( 3) log ( 1) log (4 )
2 4x x x
32. 4 1
log 3 2 2 log16 log44 2
x x x
33.
11
2log2 1 log3 log 3 27 02
x
x
34. 62log14log 322 xx x
35. 2
4
1 .271log12
12
1 xxx
x
36.
2
1log31log1log2log 3234 x
37.
2
1213log
2
3
xx
x
38. 3
82
2
44log4log21log xxx
39.
2 2
2 2
4 2 4 2
2 2
log x x 1 log x x 1
log x x 1 log x x 1
40. 2
93
32
273log
2
3log.
2
165log
x
xxx
41.
3
3 2 3 2
3 1log .log log log
23
xx x
x
42. 51
2log( 1) logx log2
x x
43. 2
2 2log ( 3) log (6 10) 1 0.x x
44.
21lg( 10) lgx 2 lg4
2 x
45. 2 2
3 3log ( 2) log 4 4 9x x x .
46. 4log ( 2).log 2 1xx
47. 2 2
2 2 2log ( 3 2) log ( 7 12) 3 log 3x x x x
48. 2 2 2
4 5 20log 1 log 1 log ( 1)x x x x x x
49. 2 2
3
1log (3 1) 2 log ( 1)
log 2x
x x
50. 2 2
27 93
11log ( 5 6) log log ( 3)
2 2
xx x x
51. 2 2log (2 4) log 2 12 3x xx
52. 0)4(log)2(log2 233 xx
53. 2 3
4 82log (x 1) 2 log 4 x log (4 x)
Phương pháp 2: Đặt ẩn phụ.
1. 155log.15log
1
255
xx
2. ( 1) 2log 16 log ( 1)x x
3. 2
2 2log 2log 2 0x x
4. 2 23 log log (8 ) 1 0x x
5. 2 11 log ( 1) log 4xx
6. 2 2log 16 log 64 3xx
7. 2 2
3log (3 ).log 3 1xx
8. 2 2log (2 ) log 2
xxx x
9.
2
5 5
5log log ( ) 1xx
x
10. 2 2log 2 2log 4 log 8x x x
11. 1
3 3log (3 1).log (3 3) 6x x
12. 2 2
1 2 1 3log (6 5 1) log (4 4 1) 2 0x xx x x x
13. 2log(10 ) log log(100 )4 6 2.3x x x
14. 2 2 2log 9 log log 32.3 xx x x
15.
3 32 2
4log log
3x x
16. 2
2 2log ( 1) 6log 1 2 0x x
17. 94log log 3 3xx
18. 4 2 2 3log ( 1) log ( 1) 25x x
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
5 Traàn Quang Time goes, you say? Ah, no! Alas, time stays, we go
19. 2 2log 2 log 4 3x
x
20. 1
5 25log (5 1).log (5 5) 1x x
21. 2
2 2 2log 2 log 6 log 44 2.3x xx
22. 2 2
2 1 1log (2 1) log (2 1) 4x xx x x
23. 2 2
3 7 2 3log (9 12 4 ) log (6 23 21) 4x xx x x x
24. 2 2log log 2(2 2) (2 2) 1x xx x
25. 3 33 log log 1 0x x
26. 2 2
2log 4 .log 12x x x
27. 2 4log 4 log 5 0x x
28. log logx x 3 3
2 2
4
3
29. 051loglog 2
323 xx
30. 3 3log 3 log log 3 log 1/ 2x xx x
31. 2 2log ( 2) log 2
xxx x
32. 2 2
3 7 2 3log (9 12 4 ) log (6 23 21) 4x xx x x x
33. 2 11 log ( 1) log 4xx
34. xxxx x 24
244
2 log2
log2log2log
35. 633log33log.log33
xx
36. 2
5 5
5log log 1x x
x
37. 2 2
3 3log log 1 5 0x x
38. 2 3log log 2 0x x
39. 1 2
14 log 2 logx x
40. 16 23log 16 4log 2logx x x
41. 2 2log 16 4log 64 3xx
42. 4 2 2 4log log log log 2x x
Phương pháp 3.
Sử dụng tính đơn điệu của hàm số
1. 5log ( 3) 4x x
2. 3log ( 3) 8x x
3. 0,5
1 3log
4 2x x
4. 2
2 2log (x x 6) x log (x 2) 4
5. 2log( 12) log( 3) 5x x x x
6. 2 2 2ln( 1) ln(2 1)x x x x x
7. 2log2.3 3xx
10 . 2 3log 2 1 log 4 2 2x x
11. 3 2log 2 log 3 2x x
12. 3 5log ( 1) log (2 1) 2x x
13. 3 24( 2) log 2 log 3 15( 1)x x x x
Phương pháp 4:
Phương trình tích và đặt ẩn phụ không
toàn phần.
1. 0)(log).211( 2
2 xxxx
2. xxxx 26log)1(log 222
3. 112log.loglog2
33
2
9 xxx
4.
6 3 2 2 2
2 2 2 2
1log (3 4) .log 8log log (3 2)
3x x x x
5. 2
3 33 log 2 4 2 log 2 16x x x x
6. 2 3 2 3log .log 1 log logx x x x
7. 2 3 2 3log .log log logx x x x
8. 2 2 2
4 5 20log ( 1).log ( 1) log ( 1)x x x x x x
9. 2
2 2log ( 3).log 2 0x x x x
10. 2
3 3(log 3) 4 log 0x x x x
11. 3logloglog.log 2
3332 xxxx
12. 0161log141log2 3
23 xxxx
13. 0621log51log 3
23 xxxx
14. 2 2 2 2 21 log 1 4 2 1 .log 1 0x x x x
15. xxxx 7272 log.log2log2log
16. 2
3 3log ( 12)log 11 0x x x x
17. 2
2 2log 2( 1)log 4 0x x x x
Phương pháp 5: Mũ hóa
1. xxx
4
4
6loglog2
2. xx
57log2log
3. xx
32log1log
4. 2 2
3 2log ( 2 1) log ( 2 )x x x x
5. 3 22log tan log sinx x
6. 2 2 3 3log log log logx x
7. x x x2 3 3 2 3 3
log log log log log log
8. 2 3 4 4 3 2log log log log log logx x
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
6 Traàn Quang Lost time is never found again
9. 2 3 5
2 3 2 5 3 5
log .log .log
log .log log .log log .log
x x x
x x x x x x
Phương pháp 6:
PP đánh giá và dùng hàm đặc trưng.
1.
2 2 3
2 2
1log (2 ) log 3 2
2x x x x
2. 3
2log 12 2
2 23 2 log ( 1) logxx x x
3. 2 2
5 52 log ( 4) logx x x x x
4.
22
2 2
1log 3 2
2 4 3
x xx x
x x
5.
1 113 7
log 30 3 3.74.7 30
x xx x
x
6. 2
2
2015 2
3log 3 2
2 4 5
x xx x
x x
7. 14217
542
3log
2
2
2
3
xx
xx
xx
8.
2 11 2
2 22 .log ( 1) 4 .(log 1 1)xx x x
9. sin( )
4 tan
x
e x
10. 2 1 3 2
2
3
82 2
log (4 4 4)
x x
x x
11. 2 3
1log 2 4 log 8
1x
x
BAÁT PHÖÔNG TRÌNH MUÕ
1.2 23 27x x
2. 152
log3
x
x
3.
11 1( 5 2) ( 5 2)
xx x
4.
2 2 161 1( ) ( )3 9
x x x
5.
1
21 1
216
xx
6.1 2 1 22 2 2 3 3 3x x x x x x
7.2 2 23 2 3 3 3 42 .3 .5 12x x x x x x
8.
3 1
1 3( 10 3) ( 10 3)x x
x x
9.
2
1 3 9x x
10. 2 25 6
1 1
33xx x
11.
22 72 1
x xx
12. 1 12 2 3 3x x x x
13. 1 1( 2 1) ( 2 1)
xx x
14.
2
1
2 13
3
x x
x x
15. 9 2.3 3 0x x
16. 2 6 72 2 17 0x x
17. 32 2 9x x
18. 2.49 7.4 9.14x x x
19. 5.2 7. 10 2.5x x x
20. 14 3.2 4x x x x
21. 2 2 22 2 26.9 13.6 6.4 0x x x x x x
22. 2 1 24 .3 3 2 .3 2 6x x xx x x x
23.
28.3 21
3 2 3
xx
x x
24. 922 7 xx
25. 12
3
13
3
11
12
xx
26. 4loglog .3416 aa xx
27. xxxxxx
2
22
153215 1
28. 09.93.83 442 xxxx
29. 13.43 2242
xx x
30. 8log.2164 41 xx
31.
52824 3
12
12
x
xx
32. 02
2
1212
32
12
x
x
33.
1 1 1
9.4 5.6 4.9x x x
34. xxxx 993.8 144
35. 112 x
xx
36. 2 2 22 2 26.9 13.6 6.4 0x x x x x x
37. xx xxxxxxx 3.43523.22352 222
38. 62.3.23.34 212 xxxx xxx
39. 1
11
1525
x
xx
40. 222 21212 15.34925 xxxxxx
41. 105 5
2
5 loglog xx x
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
7 Traàn Quang Time goes, you say? Ah, no! Alas, time stays, we go
42.
12log
log
1
1
3
3512,0
x
x
x
x
43. 13.43 2242
xx x
44.
15
9log33loglog 33log.2
2
2
1
xx
45. 126 626 loglog xx x
46. 125.3.2 2log1loglog 222 xxx
47. 23.79 1212 22
xxxxx
48. 324log2 xx
49. 1282.2.32.4222 212 xxxx xxx
50. 01223 2121
xxx
BAÁT PHÖÔNG TRÌNH LOGARIT
1. 2
1
18log
2
2
x
xx
2.
123log 2
2
1 xx
3. 243log1243log 2
32
9 xxxx
4. 3
1
6
5log 3
x
xx
5. 2
1
1
12log4
x
x
6. 2
4
1log
xx
7.
xx
xx 2
2
122
32
2
142 log.4
32log9
8loglog
8.
xxxxx 2log1244log22
12
2
9. 154log 2 x
x
10. 48loglog 22 xx
11. 01628
1
5log134 2
52 xx
x
xxx
12. 03log7164 3
2 xxx
13.
3log2
12log65log
3
1
3
12
3 xxxx
14. 1
1
32log3
x
x
15. xxxx 3232 log.log1loglog
16.
1log
1
132log
1
3
12
3
1
xxx
17. 23log 22 xx
18. 24311log 2
5 xx
19.
264log 2
2
1 xx
20.
xx 2log1log 2
2
1
21.
1log12
96log 2
2
2
1
x
x
xx
22.
18
218log.218log 24
xx
23. 193loglog 9 x
x
24.
15log1log1log3
3
1
3
1 xxx
25. 13log 23
xxx
26. 12log 2 xxx
27.
xxx
xxx x
2log2242141
21272 22
28. 2385log 2 xxx
29. 2 2
3 2log ( 2 1) log ( 2 )x x x x
30.
4
3
16
13log.13log
4
14
xx
31. 015log 3,0 xx
32.
0
352
114log114log2
3211
225
xx
xxx
33.
2
3
2
94
1loglog
xx
34. 2
1
2
54log 2
x
xx
35.
3
2
1
2
1 21log1log2
1xx
36. 1log
2
1log
2
32
34 xx
37.
014log
5
2
x
x
38. 22log1log 22
2 xx
39.
x
x
x
2log1
12
6 2
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
8 Traàn Quang Lost time is never found again
40.
0
82
1log
2
2
1
xx
x
41.
xx8
1
2
8
1 log41log.91
42. 164loglog 2 x
x
43. xxxx 5353 log.logloglog
44.
23log
89log
2
22
x
xx
45.
2log
1log22log
2
2
x
x x
46. 1
1
12log
x
xx
47.
1log1
log1
3
23
x
x
48. 1log2log
4
34
32 xx
49.
35log
35log
5
35
x
x
50. 2
1122log 2
12
xxxx
51. 2log
2
1log
77 xx
52.
0
43
1log1log2
3
3
2
2
xx
xx
53.
2
2lglg
23lg 2
x
xx
54. 2
3log 5 18 16 2
xx x
55. 316log64log 22
xx
56.
0loglog 2
4
12
2
1 xx
57. 2log2log12
xxx
58.
1log.112
1log1log.2
5
15225
x
xx
59. 232log1232log 2
22
4 xxxx
60.
xx
xx 2
2
122
32
2
142 log4
32log9
8loglog
61.
3log53loglog 24
2
2
122 xxx
62.
73log219log 1
2
11
2
1 xx
63. 3 3log x log x 3 0
64.
21 4
3
log log x 5 0
65.
21 5
5
log x 6x 8 2log x 4 0
66.
1 x
3
5log x log 3
2
67. x 2x 2log 2.log 2.log 4x 1
68. 2 2log x 3 1 log x 1
69.
8 1
8
22log (x 2) log (x 3)
3
70.
3 1
2
log log x 0
71. 5 xlog 3x 4.log 5 1
72.
2
3 2
x 4x 3log 0
x x 5
73.
1 3
2
log x log x 1
74. 2
2xlog x 5x 6 1
75.
2
23x
x 1
5log x x 1 0
2
76.
x 6 2
3
x 1log log 0
x 2
77. 2
2 2log x log x 0
78.
x x216
1log 2.log 2
log x 6
79. 2
3 3 3log x 4log x 9 2log x 3
80.
2 41 2 16
2
log x 4log x 2 4 log x
81. 224log12log 32 xx
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
9 Traàn Quang Time goes, you say? Ah, no! Alas, time stays, we go
HEÄ PHÖÔNG TRÌNH MUÕ - LOGARIT
I. Hệ phương trình mũ.
1.
13
35
4
yx
yx
xy
xy
2.
yxyx
x
y
y
x
33 log1log
324
3.
423
99.3
1 2
1
y
x
x
yx
y
x
y
4.
y
y
y
x
x
y
y
x
12
3
5
2
3.33
2.22
5.
2lglg
122 yx
xy
6.
723
7723
2
2
yx
yx
7.
2
log.2
loglog
43
xxy
yy
yx
xy
8.
1932
63.22.311 yx
yx
9.
33
3
3.55
5
yx
yx
yx
yx
10.
y
yy
x
xx
x
22
24
4521
23
11.
068
13.4
4
4
4
yx
xy
yx
yx
12.
3lg4lg
lglg
34
43
yx
yx
13.
1log
.3log
4
2
5log
xyy
xy
y
xxy
14.
113
2.322
2
3213
xxyx
xyyx
15.
3
81log2log
142
21 xy
yxyx
yx
16.
421223
421223xy
yx
17.
x y
3x 2y 3
4 128
5 1
18.
2
x y
(x y) 1
5 125
4 1
19.
2x y
x y
3 2 77
3 2 7
20.
x y2 2 12
x y 5
21.
3 2
1
2 5 4
4 2
2 2
x
x x
x
y y
y
13 2
3 9 18
y
y
x
x
22.
23.
2 2
12 2x y x
x y y x
x y
24.
2 1
2 1
2 2 3 1
2 2 3 1
y
x
x x x
y y y
II.Hệ phương trình lôgarit
1)
16
2loglog33
22
yx
xyxyyx
2)
3lg4lg
lglg
34
43
yx
yx
3)
1log
3log2loglog
7
222
yx
yx
4)
8
5loglog2
xy
yx xy
5)
1loglog
4
44
loglog 88
yx
yx xy
6)
1loglog
4
44
loglog 88
yx
yx xy
7)
1log
433.11
3 yx
x
xx y
8)
xx
yx
4224
2442
loglogloglog
loglogloglog
9)
3
81log2log
142
21 xy
yxyx
yx
10)
223log
223log
xy
yx
y
x
BAØI TAÄP PT - BPT - HPT Logarit vaø Muõ
10 Traàn Quang Lost time is never found again
11)
453log.53log
453log53log
xyyx
xyyx
yx
yx
12)
02
0loglog2
1
23
32
3
yyx
yx
13)
1loglog
272
33
loglog 33
xy
yx xy
14)
9loglog.5
8loglog.5
43
2
242
yx
yx
15)
0lg.lglg
lglglg2
222
yxyx
xyyx
16)
14log5log
612log22log.2
21
221
xy
xxyxxy
yx
yx
17)
1log4224log1log
3log12loglog
42
44
4422
4
y
xxyyxy
yxxyx
18)
1233
2422
2loglog 33
yxyx
xyxy
19)
yxyx
y
x
x
y
33 log1log
324
20)
yyy
yxx 813.122
3log2
3
21)
2log
4log
2
1
2
y
x
xy
22)
01422
22
32
222
12
2
xyxxyx
xy yx
x
23)
2 2
lgx lgy 1
x y 29
24)
3 3 3log x log y 1 log 2
x y 5
25)
2 2lg x y 1 3lg2
lg x y lg x y lg3
26)
4 2
2 2
log x log y 0
x 5y 4 0
27)
x y
y x
3 3
4 32
log x y 1 log x y
28)
y
2x y
2log x
log xy log x
y 4y 3
29)
2 2
2 2
2 2log ( ) 1 log ( )
3 81x xy y
x y xy
30)
1 4
4
2 2
1log ( ) log 1
25
y xy
x y
31) 2 3
9 3
1 2 1
3log (9 ) log 3
x y
x y
32) 3 3
3 .2 972
log ( ) 3
x y
x y
33) 2
log log 2
12
y xx y
x y
34) 3 3
4 32
log ( ) 1 log ( )
x y
y x
x y x y
35)
41 log
4096y
y x
x
36) 4 2
4 3 0
log log 0
x y
x y
37) 5
3 .2 1152
log ( ) 2
x y
x y
38)
2 2
1 1
1 1
log (1 2 ) log (1 2 ) 4
log (1 2 ) log (1 2 ) 2
x y
x y
y y x x
y x
39)
3 3log ( ) log 2
2 2
4 2 ( )
3 3 22
xy xy
x y x y
40) 2 2
ln(1 ) ln(1 )
12 20 0
x y x y
x xy y
Top Related