523 bài tập PT-BPT-HPT mũ - Logarit (Phân theo 15 dạng ôn thi đại học)

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


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



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.



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



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



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



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



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



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



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

523 bài tập PT-BPT-HPT mũ - Logarit (Phân theo 15 dạng ôn thi đại học)

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Transcript of 523 bài tập PT-BPT-HPT mũ - Logarit (Phân theo 15 dạng ôn thi đại học)