Hướng dẫn giải bài tập phương trình mũ

BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go PHƯƠNG TRÌNH MŨ : Đưa về cùng cơ số 1.     x x x 2 3 2 1 2 16 2.   2 x 6x 5/2 2 16 2 3.   2 x 4x 3 1 / 243 4. 5 17 73 32 0 25 128,.    xx xx 5. 3 4 2 8 3 5 125 /xx  6. 21 48 xx  7. x x 1 x 2 2 .3 .5 12   8. 2 9 27 3 8 64              xx 9.   x x x        2 1 1 3 2 2 2 4 10. 2 2 5 2 1 3 27     x x x 11. 1 2 1 4.9 3 2   xx 12. 3x 1 5x 8 (2 3) (2 3) 13. x1 x1 x1 ( 5 2) ( 5 2) 14. 1 3 3 1 ( 10 3) ( 10 3) x x x x 15. 3 1 2 1 3 2 4 8 2 2 0 125. . . ,     x x x 16. 3 3 3 2 4 0 125 4 2,  xx x 17. 4 2 4 22 4 5 .0,2 125.0,04 x x x xx x      18. 4 1 2 3 2 5.4 2 16 3 x xx      19. 2( 1) 1 2 3.2 7 x x    20. 3 3 1 1 2 .3 2 .3 192 x x x x  21. 2 2 3 1 3 3 9 27 675 x xx    22. 2 2 2 2 1 1 2 2 3 3 2 x x x x      23. 22 3 9 9 4 16 16      x x 24. x xx 2 21 ( 1) 1 25. 23 3 3 1 9 27 81 3 x x x x       26. 2 1 1 11 3.4 .9 6.4 .9 32 x x x x      27.       x 4 x 3 x x 2 3 5 3 5 28.        x 1 x 2 x 4 x 3 7.3 5 3 5 29. x x 1 x 2 x x 1 x 2 2 2 2 3 3 3          30.   3 2 9 2 2222 2   xxxx x 31.   2 cos 1 2 cos 22 xx x x x x   : Đặt ẩn phụ. 1. 2 16 15 4 8 0   xx 2. 9 8.3 7 0   xx 3.     2x 8 x 5 3 4.3 27 0 4. 1 4 2 4 2 2 6 x x x      5. 22 4 6.2 8 0 xx    6. 2 7 6.0,7 7 100 x x x  7. 13 3 64 2 12 0 xx     8. 22 2 1 2 4 5.2 6 0 x x x x        9. 22 4 16 10.2 xx  10. log log5 25 5 4. x x 11. 22 33 2log ( 16) log ( 16) 1 2 2 24 xx    12. 22 12 9 10.3 1 0 x x x x       13. 2x 6 x 7 2 2 17 0     14.     10 5 10 3 3 84 xx  15. 2 1 1 1 .4 21 13.4 2 xx  16. 3 2cos 1 cos 4 7.4 2 0 xx    17. 22 5 1 5 4 12 2 8 0.         x x x x 18. 3033 22   xx 19. x 1 3 x 5 5 26   20. D03 x x x x    22 2 2 2 3 21. 22 sin cos 9 9 10 xx 22. 31 53 5.2 3.2 7 0 x x      23. 12 5 5.0,2 26   xx 24. 1 4 4 3.2 x x x x  25. 22 sin cos 2 5.2 7 xx 26. 2 cos2 cos 4 4 3 xx  27. 1 5 5 4 0 xx 28. 2 2 2 2 1 2 2 1 9 34.15 25 0          x x x x x x 29. 1 1 1 x x x 2.4 6 9 www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Lost time is never found again 30. 1 1 1 6.9 13.6 6.4 0 x x x 31. 3 3 3 25 9 15 0 x x x 32. A06 027.21812.48.3 xxxx 33. 07.714.92.2 22 xxx 34. x x x 6.9 13.6 6.4 0 35. 27 12 2.8 x x x 36. /2 4.3 9.2 5.6 x x x 37. 2 2 2 15.25 34.15 15.9 0 x x x 38. 25 12.2 6,25.0,16 0 x x x 39. 31 125 50 2 x x x 40. xxx 27.2188 41. 2 3 2 3 14 xx 42. 2 3 2 3 2 xx 43. 4 15 4 15 8 xx 44. xx (2 3) (2 3) 4 0 45. B07 ( 2 1) ( 2 1) 2 2 0 xx 46. ( 3 2) (7 4 3)(2 3) 4(2 3) xx 47. 02.75353 x xx 48. x x x 3 (3 5) 16(3 5) 2 49. xx (7 4 3) 3(2 3) 2 0 50. 26 15 3 2 7 4 3 2 2 3 1 x x x 51. cos cos 5 7 4 3 7 4 3 2 xx 52. 7 3 5 7 3 5 14.2 xx x 53. xx ( 2 3) ( 2 3) 4 54. xx 7 3 5 7 3 5 78 22 55. 10245245 xx 56. 3 7 5 21 5 21 2 xx x 57. xx 7 4 3 7 4 3 14 58. 10625625 tantan xx 59. xx x 3 5 21 7 5 21 2 60. sin sinxx 5 2 6 5 2 6 2 61. 3 31 81 2 6 2 1 22 xx xx 62. x x x x22 5 2 2 2 2 20 16 63. 11 3 3 9 9 6 x x x x 64. x x x x1 3 2 8 8.0,5 6.2 125 24.0,5 65. 64)5125.(275.95 3 xxxx 66. 2 2 6 2 6 xx 67. xxx 9133.4 13 68. 093.613.73.5 1112 xxxx 69. 24223 2212.32.4 xxxx 70. 2 2 1 2 1 4 2 3 2 3 23 x x x 71. 22 ( 1) 2 1 101 (2 3) (2 3) 10(2 3 ) x x x 72. 3 1 2 2 7.2 7.2 2 0 x x x S dng tớnh n iu ca hm s 1. 4 9 25 x x x 2. x x x 3 4 5 3. x 3 x 4 0 4. x x 4115 5. 2 2 2 2 3 2 2 xx xx 6. /2 2 3 1 xx 7. x x x 3.16 2.8 5.36 8. x xxx 202459 9. 1/ 52 2,9 25 xx 10. 2 3 2 3 2 xx x 11. 3 2 3 2 10( ) ( ) x xx 12. xxx 5.22357 13. xx xx 2.1.24 2 2 14. x x 6 217.9 15. 32 1 1 1 5 4 3 2 2 5 7 17 2 3 6 x x x x x x x x x x 16. 2 4 2 2 3 ( 4)3 1 0 xx x 17. 3 .2 3 2 1 xx xx 18. 1 1 5 3 5 3 10 3 4 12 x x x xx x 19. 1 1 1 3 2 2 6 3 2 6 x x x xx x 20. 2013 2015 2.2014 x x x www.VNMATH.com BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go 4: Đưa về phương trình tích và Đặt ẩn phụ khơng tồn phần. 1. xxx 6132  2. 8.3 x + 3.2 x = 24 + 6 x 3. 2 1 1 5 7 175 35 0 x x x     4. D06 0422.42 2 22   xxxxx 5. 22 2 ( 4 2) 4 4 4 8 x x x x x       6. 2 1 2 4 .3 3 2 .3 2 6 x x x x x x x       7. 20515.33.12 1  xxx 8. 2 2 2 3 2 6 5 2 3 7 4 4 4 1          x x x x x x 9.   02.93.923 2  xxxx 10.     021.2.23 2  xx xx 11.   0523.2.29  xx xx 12.   035.10325.3 22   xx xx 13.   1224 2 22 11   xxxx 14. 22 2 1 2 2 2 9.2 2 0 x x x x      15. 2 2 2 .2 8 2 2 xx xx     16. 2 2 2 2 .6 6 .6 6 x x x x xx       17. 3 2 3 4 2 1 2 1 .2 2 .2 2 xx xx xx         18.   9 2 2 .3 2 5 0 xx xx     19.     xx xx     2 3 2 2 1 2 0 20. 3.4 (3 10)2 3 0 xx xx 21. 22 3.16 (3 10)4 3 0 xx xx       22. ► 2 3 1 3 4 2 2 16 0 x x x     23. ► x x x x      4 1 3 2 1 5 25.5 26.5 5 5 0 24. ► x x x x      1 81 4.27 10.9 4.3 3 0  Lơgarit hóa 6: Hàm đặc trưng và PP đánh giá. 1. 2112212 532532   xxxxxx 2. 2 22 1 1 2 2 22 2 xx xx x x 3. 1 2 4 1 xx x     4.   2 11 124 2   x xx 5. x xxxx 3cos.722 322 cos.4cos.3   6.     134732 1   x xx 7. x x21 8. x x3 2 1 9. x x     1 1 22 10. 123223 1122   x xxx xx 11.   x x x   1 2cos 22 2 12. x x 2cos3 2  13. 2 cos 2 33 x x 14. 4 2 16 2 2 xx x     15. 2 3 2 6 9 4 x xx        16. 2 2 1 2 xx x x   17. 4 6 25 2 xx x   18. 3 5 6 2   xx x 19. xx x  3 2 3 2 20. xx x    2 3 2 3 2 21. 2 2 2 2 3 4 3 x x x    22. 2 2 2 2 2 1 2 3 7 8 4 x x x x x     23. 2 2 2 2 4.10 7 3 x x x    24. 8.3 3.2 24 6 x x x    PHƯƠNG TRÌNH LOGARIT : Đưa về cùng cơ số 1. 2 log (5 1) 4x  2. 2 5 log ( 2 65) 2 x xx     3. 2 2 log 1 xx x   4. 2 2 1/2 log ( 1) log (x 1)x    9. 4 1 3 2 21 57 xx              10. 32 23 xx  11. 2 5 6 3 52 x x x 12. 2 5 .3 1 xx  13. 231224 3.23.2   xxxx 14. 3 2 3 .2 6 x x x  15. 1 2 .5 10 x x x 16. 22 3 2 6 2 5 2 3 3 2 x x x x x x        1. 1 5 . 8 100 xx x  2. 2 2 .3 9 xx 3. 2 2 8 36.3 x x x 4. 1 2 1 4.9 3 2 xx  5. 2 2 2 .3 1,5 x x x  6. 21 1 5 .2 50 x x x    7. 43 34 xx 8. 75 57 xx  www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Lost time is never found again 5. 55 log ( 3) log ( 2 6)xx 6. log 2 3 1 3 1 2 2 x xx 7. 22 log 6 log 3 1xx 8. 4 15 2 22 2 2 log 36 log 81 log 3 log 4 xx 9. 3 9 27 log log log 11x x x 10. 33 log log ( 2) 1xx 11. 93 log ( 8) log ( 26) 2 0xx 12. 2 22 log ( 3) log (6 10) 1 0xx 13. 32 1 log( 1) log( 2 1) log 2 x x x x 14. 3 4 1/16 8 log log log 5x x x 15. 3 22 log (1 1) 3log 40 0xx 16. 2 5 5 log (4 6) log (2 2) 2 xx 17. 34 1/3 3 3 log log log 3 3x x x 18. 2 5 0,2 5 0,04 log ( 1) log 5 log ( 2) 2log ( 2)x x x 19. 2 3 3 1/4 0,25 1/4 3 log ( 2) 3 log (4 ) log ( 6) 2 x x x 20. 3 loglog log(log 2) 0xx 21. 2 log 1 3log 1 2 log 1x x x 22. 42 log ( 3) log ( 7) 2 0xx 23. 21 8 log ( 2) 6log 3 5 2xx 24. 3 18 2 2 log 1 log (3 ) log ( 1)x x x 25. 21 2 2log 2 2 log 9 1 1xx 26. 4 log ( 2).log 2 1 x x 27. 2 9 log 27.log 4 x x x x 28. 22 33 log ( ) log ( ) 3xx xx 29. 22 2 2 2 log ( 3 2) log ( 7 12) 3 log 3x x x x 30. 2 9 3 3 2log log .log ( 2 1 1)x x x 31. 5 3 5 9 log log log 3.log 225xx 32. 2 3 3 log 1 log 2 1 2xx 33. 23 48 2 log ( 1) 2 log 4 log ( 4)x x x 34. 2 2 2 2 3 2 3 log ( 1 ) log ( 1 ) 0x x x x 35. 22 93 3 11 log ( 5 6) log log 3 22 x x x x 36. 42 21 11 log ( 1) log 2 log 4 2 x xx 37. 2 22 5 log log ( 25) 0 5 x x x 38. 5 log 5 4 1 x x 39. 44 2 log 2 ( 3) log 2 3 x xx x 40. 23 48 2 log 1 2 log 4 log 4x x x 41. 2 66 11 1 log log 1 72 x x x 42. 2 3 1 log 3 1 2 2 x xx 43. 2 33 2log ( 2) log ( 4) 0xx 44. log9 log 96 x x 45. 5 5 50 log log x x 46. 2 log 1 log 6 5 x x 47. 3 16 3 log 9 log x x xx 48. 2 22 log 10 1 log4 log2 log (3 2) 2 log 5 xx x 49. 2 log 9 2 1 3 x x 50. log ( ) log ( ) xx x 1 4 4 2 3 21 2 51. 2 2 1 2 2 1 log ( 1) log ( 4) log (3 ) 2 x x x 52. D07 22 1 log (4 15.2 27) 2log 0 4.2 3 xx x 53. 8 42 2 11 log ( 3) log ( 1) log (4 ) 24 x x x 54. 4 1 log 3 2 2 log16 log 4 42 xx x 55. 1 1 2log2 1 log3 log 3 27 0 2 x x 56. 3 22 log 4 1 log 2 6 xx x www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go 57. 2 1 4 log 1 7 2. 1 21 21 xx x x 58. 4 3 2 3 1 log 2 log 1 log 1 3log 2 x 59. 22 22 4 2 4 2 22 log x x 1 log x x 1 log x x 1 log x x 1 60. 5 1 2log( 1) logx log 2 xx 61. 2 22 log ( 3) log (6 10) 1 0.xx 62. 2 1 log( 10) logx 2 lg4 2 x 63. 22 33 log ( 2) log 4 4 9x x x 64. 39 3 4 2 log log 3 1 1 log x x x 65. 22 3 1 log (3 1) 2 log ( 1) log 2 x xx 66. 22 log (2 4) log 2 12 3 xx x : t n ph. 1. 23 log log 2 0xx 2. 2 22 log 2log 2 0xx 3. 22 3 log log (8 ) 3 0xx 4. 2 4 2 1 2 log 1 log log 0 4 xx 5. 1 33 log (3 1).log (3 3) 6 xx 6. 1 5 25 log (5 1).log (5 5) 1 xx 7. 3 3 22 4 log log 3 xx 8. 4 2 2 3 log ( 1) log ( 1) 25xx 9. 9 4log log 3 3 x x 10. ( 1) 2 log 16 log ( 1) x x 11. 21 1 log ( 1) log 4 x x 12. 2 2 log 16 log 64 3 x x 13. 22 3 log (3 ).log 3 1 x x 14. 2 2 log (2 ) log 2 x x xx 15. 2 55 5 log log ( ) 1 x x x 16. 2 2 log 2 2log 4 log 8 xx x 17. 2 2 3 27 16log 3log 0 x x xx 18. 2 2 1/2 2 log 4 log 8 8 x x 19. 23 /2 4 2 4 log 2log 3log x x x x x x 20. 2 3/ 3 log 2 log 1 x x 21. 16 2 3log 16 4log 2log x xx 22. 23 /2 4 16 log 40log 14log 0 x x x x x x 23. 22 1 2 1 3 log (6 5 1) log (4 4 1) 2 0 xx x x x x 24. 22 3 7 2 3 log (9 12 4 ) log (6 23 21) 4 xx x x x x 25. A08 22 2 1 1 log (2 1) log (2 1) 4 xx x x x 26. 2 log(10 ) log log(100 ) 4 6 2.3 x x x 27. 2 2 2 2 log 2 log 6 log 4 4 2.3 xx x 28. 2/ 2 log 2 log 4 3 x x 29. 22 2 log 4 .log 12 x xx 30. 24 log 4 log 5 0xx 31. 22 33 log log 1 5 0xx 32. 33 log 3 log log 3 log 1/ 2 x x xx 33. 44 4 2 2 2 log 2 log 2 log log 2 x x x x x 34. 33 log . log 3 3 log 3 3 6 x x 35. 4 2 2 4 log log log log 2xx 36. 8 2 3log log 2 2 5 0 x x xx 37. 12 1 4 log 2 logxx 38. 2 1 log( 1) 2 2 1 log( 1) 1 log ( 1) x x x 39. 24 1 log 4 log 2 4xx 40. 2 22 log ( 1) 6log 1 2 0xx S dng tớnh n iu ca hm s 1. 5 log ( 3) 4xx 2. 3 log ( 3) 8xx 3. 0,5 11 log 42 xx 4. 2 22 log (x x 6) x log (x 2) 4 www.VNMATH.com BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Lost time is never found again 5. 2 log( 12) log( 3) 5x x x x      6. 2 log 2.3 3 x x  10 .     23 log 2 1 log 4 2 2 xx     11.     32 log 2 log 3 2xx    12. 35 log ( 1) log (2 1) 2xx    13.     32 4( 2) log 2 log 3 15( 1)x x x x        x xx    2 2 log ( 2) 6 21  :   2 4 4 1 1 x x  có đúng 3 nghiệm thực phân biệt. 4: Phương trình tích và đặt ẩn phụ khơng tồn phần. 1. 0)(log).211( 2 2  xxxx 2. xxxx 26log)1(log 2 2 2  3.   112log.loglog2 33 2 9  xxx 4. 6 3 2 2 2 2 2 2 2 1 log (3 4) .log 8log log (3 2) 3 x x x x    5.         2 33 3 log 2 4 2 log 2 16x x x x      6. 2 3 2 3 log .log 1 log logx x x x   7. 2 3 2 3 log .log log logx x x x 8. 2 2 2 4 5 20 log ( 1).log ( 1) log ( 1)x x x x x x       9. 2 22 log ( 3).log 2 0x x x x     10. 2 33 (log 3) 4 log 0x x x x     11. 3logloglog.log 2 3 332  xxxx 12.         0161log141log2 3 2 3  xxxx 13.       0621log51log 3 2 3  xxxx 14.         2 2 2 2 2 1 log 1 4 2 1 .log 1 0x x x x      15. xxxx 7272 log.log2log2log  16. 2 33 log ( 12)log 11 0x x x x     17. 2 22 log 2( 1)log 4 0x x x x    18. 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   19. 3 3 2 3 2 31 log .log log log 2 3 x xx x    20. 22 log log 2 (2 2) (2 2) 1 xx xx     21.   2 2 2 2 6 1/6 .log 5 2 3 log 5 2 3 2x x x x x x x x       22. 3 2 3 3 2 log .log log log 3x x x x 23.       22 2 1 1 2 3 .log 1 2 log 2 3 .log 2 2log 1 xx x x x x         24.     2 2 7 7 2 log log 3 / 2 2 log 3 logx x x x x x        25.     1 4 2 2 2 1 sin 2 1 2 0 x x x x y         5: Mũ hóa 1.   x x x 4 4 18 2log log 2.   xx 57 log2log  3.   xx 32 log1log  4. 22 32 log ( 2 1) log ( 2 )x x x x    5. 32 2log tan log sinxx 6. 23 log log 1xx 7. 53 log log log15xx 8. 2 2 3 3 log log log logxx 9. x x x 2 3 3 2 3 3 log log log log log log 10. 2 3 4 4 3 2 log log log log log logxx 11. 2 2 2 log 9 log log 3 2 .3 x x x x 12. 3 2 3 log log 3 3 100. 10 xx x 13. x x x log 5 5 log 3 10 14. 2 22 log 1 2log 2 224 xx x   15. 2 log 3log 4,5 2log 10 x x x x     16. 2 2 2 log log 3 3log 36 xx x 17. 9 log 2 9. x xx 18. 2 log 22 2 2. log 2 x x xx áp 6: PP đánh giá và dùng hàm đặc trưng. 1. 2 2 3 22 1 log (2 ) log 3 2 2 x x x x    2. 3 2 log 1 22 22 3 2 log ( 1) log x x x x      3. 22 55 2 log ( 4) logx x x x x     4. 2 2 2 ln( 1) ln(2 1)x x x x x      www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go 5. 2 2 2 2 1 log 3 2 2 4 3 xx xx xx 6. 11 1 37 log 30 3 3.7 4.7 30 xx xx x 7. 2 2 2015 2 3 log 3 2 2 4 5 xx xx xx 8. 2 2 3 2 3 log 7 21 14 2 4 5 xx xx xx 9. 2 1 12 22 2 .log ( 1) 4 .(log 1 1) x x xx 10. sin( ) 4 tan x ex 11. 2 1 3 2 2 3 8 22 log (4 4 4) xx xx 12. 23 1 log 2 4 log 8 1 x x 13. 2 21 log 1 2 x x x x 14. log 1 lg 4,5 0 x x A02: Cho phng trỡnh 22 33 log log 1 2 1 0x x m (1) (m l tham s) a) Gii phng trỡnh (1) khi m = 2. b) Tỡm m phng trỡnh (1) cú ớt nht mt nghim thuc on 3 1 ; 3 . www.VNMATH.com BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Lost time is never found again BẤT PHƯƠNG TRÌNH MŨ 1. 2 2 3 27 xx  2. 15 2 log 3   x x 3. 1 1 1 ( 5 2) ( 5 2) x x x       4. 2 2 16 11 ( ) ( ) 39 x x x  5. 1 2 1 1 2 16 x x       6. 1 2 1 2 2 2 2 3 3 3 x x x x x x         7. 2 2 2 3 2 3 3 3 4 2 .3 .5 12 x x x x x x       8. 31 13 ( 10 3) ( 10 3) xx xx      9. 2 1 3 9 xx  10. 2 2 56 11 3 3 x xx    11.   2 27 21 xx x   12. 11 2 2 3 3 x x x x    13. 1 1 ( 2 1) ( 2 1) x x x      14. 2 1 2 1 3 3 xx xx       15. 9 2.3 3 0 xx    16. 2 6 7 2 2 17 0 xx    17. 3 2 2 9 xx  18. 2.49 7.4 9.14 x x x  19. 5.2 7. 10 2.5 x x x  20. 1 4 3.2 4 x x x x  21. 2 2 2 2 2 2 6.9 13.6 6.4 0 x x x x x x      22. 2 1 2 4 .3 3 2 .3 2 6 x x x x x x x       23. 2 8.3 2 1 3 2 3 x x xx       24. 922 7  xx 25. 12 3 1 3 3 1 1 12                xx 26. 4loglog .3416 aa x x  27.     xx xx xx     2 2 2 153215 1 28. 09.93.83 442   xxxx 29.   13.43 224 2   xx x 30. 8log.2164 4 1   xx 31.     52824 3 12 12    x xx 32. 02 2 1 212 32 12           x x 33. 1 1 1 9.4 5.6 4.9 x x x     34. xxxx 993.8 1 44   35.   11 2  x xx 36. 2 2 2 2 2 2 6.9 13.6 6.4 0 x x x x x x      37. xx xxxxxxx 3.43523.22352 222  38. 62.3.23.34 212   xxxx xxx 39.     1 1 1 1525     x x x 40. 222 21212 15.34925 xxxxxx   41.   105 5 2 5 log log  x x x 42.       12log log 1 1 3 35 12,0           x x x x 43.   13.43 224 2   xx x 44.   15 9log33loglog 3 3 log.2 2 2 1   x x 45. 126 6 2 6 loglog  xx x 46.     125.3.2 2log1loglog 222   xxx 47. 23.79 1212 22   xxxxx 48. 32 4log 2  x x 49. 1282.2.32.4 222 212   xxxx xxx 50. 01223 2 121   x xx BẤT PHƯƠNG TRÌNH LOGARIT 1. 2 1 18 log 2 2    x xx 2.   123log 2 2 1  xx 3.     243log1243log 2 3 2 9  xxxx 4. 3 1 6 5 log 3    x x x 5. 2 1 1 12 log 4    x x 6. 2 4 1 log        x x 7. x x x x 2 2 1 2 2 3 2 2 1 4 2 log.4 32 log9 8 loglog                  www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go 8. xxxxx 2log1244log2 2 1 2 2 9. 154log 2 x x 10. 48loglog 22 x x 11. 01628 1 5 log134 2 5 2 xx x x xx 12. 03log7164 3 2 xxx 13. 3log 2 1 2log65log 3 1 3 1 2 3 xxxx 14. 1 1 32 log 3 x x 15. xxxx 3232 log.log1loglog 16. 1log 1 132log 1 3 1 2 3 1 x xx 17. 23log 2 2 xx 18. 24311log 2 5 xx 19. 264log 2 2 1 xx 20. xx 2log1log 2 2 1 21. 1log 12 96 log 2 2 2 1 x x xx 22. 1 8 218 log.218log 24 x x 23. 193loglog 9 x x 24. 15log1log1log 3 3 1 3 1 xxx 25. 13log 2 3 x xx 26. 12log 2 xx x 27. x xx x xx x 2 log2242141 2 1272 22 28. 2385log 2 xx x 29. 22 32 log ( 2 1) log ( 2 )x x x x 30. 4 3 16 13 log.13log 4 14 x x 31. 015log 3,0 xx 32. 0 352 114log114log 2 3 2 11 2 2 5 xx xxx 33. 2 3 2 9 4 1 loglog xx 34. 2 1 2 54 log 2 x x x 35. 3 2 1 2 1 21log1log 2 1 xx 36. 1log 2 1 log 2 3 2 3 4 xx 37. 0 14log 5 2 x x 38. 22log1log 2 2 2 xx 39. x x x 2log1 12 6 2 40. 0 82 1log 2 2 1 xx x 41. xx 8 1 2 8 1 log41log.91 42. 164loglog 2 x x 43. xxxx 5353 log.logloglog 44. 2 3log 89log 2 2 2 x xx 45. 2log 1 log22log 2 2 x x x 46. 1 1 12 log x x x 47. 1 log1 log1 3 2 3 x x 48. 1log2log 4 3 4 3 2 xx 49. 3 5log 35log 5 3 5 x x 50. 2 1 122log 2 1 2 xx xx 51. 2log 2 1 log 7 7 xx 52. 0 43 1log1log 2 3 3 2 2 xx xx 53. 2 2lglg 23lg 2 x xx 54. 2 3 log 5 18 16 2 x xx 55. 316log64log 2 2 x x 56. 0loglog 2 4 1 2 2 1 xx www.VNMATH.com BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ Tran Quang Lost time is never found again 57. 2log2log 12 xxx 58. 1log. 112 1 log1log.2 5 15 2 25 x x x 59. 232log1232log 2 2 2 4 xxxx 60. x x x x 2 2 1 2 2 3 2 2 1 4 2 log4 32 log9 8 loglog 61. 3log53loglog 2 4 2 2 1 2 2 xxx 62. 73log219log 1 2 1 1 2 1 xx 63. 33 log x log x 3 0 64. 2 14 3 log log x 5 0 65. 2 15 5 log x 6x 8 2 log x 4 0 66. 1x 3 5 log x log 3 2 67. x 2x 2 log 2.log 2.log 4x 1 68. 22 log x 3 1 log x 1 69. 81 8 2 2 log (x 2) log (x 3) 3 70. 31 2 log log x 0 71. 5x log 3x 4.log 5 1 72. 2 3 2 x 4x 3 log 0 x x 5 73. 13 2 log x log x 1 74. 2 2x log x 5x 6 1 75. 2 2 3x x1 5 log x x 1 0 2 76. x 6 2 3 x1 log log 0 x2 77. 2 22 log x log x 0 78. xx 2 16 1 log 2.log 2 log x 6 79. 2 3 3 3 log x 4 log x 9 2 log x 3 80. 24 1 2 16 2 log x 4log x 2 4 log x 81. 224log12log 32 xx www.VNMATH.com [...]...BÀI GIẢNG PT - BPT - HPT Logarit và Mũ www.VNMATH.com HỆ PHƯƠNG TRÌNH MŨ - LOGARIT I Hệ phương trình mũ 1 2 3 4 5 x   y4 x 5 y   x  y  3   x 3  y 1  y  xx 4 y  32  log 3 x  y   1  log 3 x  y   x 1 1 y 2y  9  9 3  ... x 1 y  x 19  2  2 y 1  x  3  2  y 3 x  9  18  20  x2  y  y 2  x   x y x 1 2  2  x  y 21   x  x 2  2 x  2  3 y 1  1   2 x 1  y  y  2 y  2  3 1 22  II.Hệ phương trình lơgarit 1) 2) 3) 4) 5) 6)  x  y  log 2 y  log 2 x 2  xy   3 3  x  y  16 3lg x  4 lg y   4 x lg 4  3 y lg 3  log 2 x  log 2 y  2  log 2 3  log 7 x  y   1 2log...  2  log 3 y  2 x   2 10)  y log x 3x  5 y   log y 3 y  5 x   4   log 3x  5 y  log y 3 y  5 x   4 11)  x Time goes, you say? Ah, no! Alas, time stays, we go BÀI GIẢNG PT - BPT - HPT Logarit và Mũ www.VNMATH.com 12) 1 2  2 log 3 x  log 3 y  0   x 3  y2  2y  0  x  2y  27  13) log 3 y  log 3 x  1 5 log 2 x  log 4 y 2  8   5 log 2 x 3  log 4 y  9 14) . www.VNMATH.com BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go HỆ PHƯƠNG TRÌNH MŨ - LOGARIT I. Hệ phương trình mũ. 1.                 13 3 5 4 yx yx x y xy . nghim thuc on 3 1 ; 3 . www.VNMATH.com BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Lost time is never found again BẤT PHƯƠNG TRÌNH MŨ 1. 2 2 3 27 xx  2. 15 2 log 3   x x . BÀI GIẢNG PT - BPT - HPT Logarit và Mũ  Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go PHƯƠNG TRÌNH MŨ : Đưa về cùng cơ