![http://www.mathvn.com
25.
log 2 ( x +1) 4( x + 1) + 2 log x +1 ( x + 1) = 5
2
26.
log 3 x - log 3 x - 3 < 0
[
)]
(
log1 / 3 log 4 x 2 - 5 > 0
28. log1 / 3 x + 5 / 2 ³ log x 3
29. log x 2. log 2 x 2. log 2 4 x > 1
27.
30.
log 3
x2 - 4x + 3
x2 + x - 5
³0
x -1 ö
æ
log x +6 ç log 2
÷>0
x + 2ø
3 è
1
32. log x 2. log x / 16 2 >
log 2 x - 6
33. log x 2 2 x ³ 1
31.
(
)
log x log 9 3 x - 9 £ 1
3x + 2
35. log x
>1
x+2
36. log 3 x - x 2 (3 - x ) > 1
34.
(
[
)
)]
log x 5 x 2 - 8 x + 3 > 2
x
38. log x log 3 9 - 6 = 1
39. 3 log x 16 - 4 log16 x = 2 log 2 x
40. log x 2 16 + log 2 x 64 = 3
37.
41.
(
1
log1 / 3 2 x 2 - 3 x + 1
1 + log 2 x
a
42.
>1
1 + log a x
43.
(
>
1
log1 / 3 ( x + 1)
(0 < a ¹ 1)
)
log a 35 - x 3
> 3 víi 0 < a ¹ 1
log a (5 - x )
2 sin x -2 cos x +1
æ1ö
-ç ÷
è 10 ø
cos x -sin x -lg 7
+ 5 2 sin x -2 cos x +1 = 0
44.
2
45.
log 5 x 2 - 4 x - 11 - log11 x 2 - 4 x - 11
³0
2 - 5 x - 3x 2
(
)
2
(
)
3
9](https://image.slidesharecdn.com/www-131026220002-phpapp02/85/Www-mathvn-com-bt-mu-logarit-mathvn-com-9-320.jpg)
Www.mathvn.com bt-mu logarit-mathvn.com
- 1. http://www.mathvn.com Bµi tËp ph-¬ng tr×nh, bÊt ph-¬ng tr×nh mò vµ logarit – phÇn 1 Bµi I: Gi¶i c¸c ph-¬ng tr×nh: 1. 2 x 2 - x +8 x2 -6x - = 41-3x 5 2 2. 2 = 16 2 x x -1 3. 2 + 2 + 2 x -2 = 3x - 3x-1 + 3x-2 4. 2 x.3x -1.5x -2 = 12 5. (x 2 - x + 1)x 2 -1 =1 6. ( x - x 2 )x-2 = 1 2 7. (x 2 - 2x + 2) 4-x = 1 Bµi II: Gi¶i c¸c ph-¬ng tr×nh: 8. 34x+8 - 4.32x+5 + 27 = 0 9. 22x+6 + 2 x+7 - 17 = 0 10. (2 + 3)x + (2 - 3)x - 4 = 0 11. 2.16 x - 15.4 x - 8 = 0 12. (3 + 5)x + 16(3 - 5)x = 2 x +3 13. (7 + 4 3)x - 3(2 - 3)x + 2 = 0 14. 3.16 x + 2.8x = 5.36 x 15. 1 2.4 x 2 8x 1 + 6x = 1 9x 3x +3 -2 x 16. + 12 = 0 x x +1 17. 5 + 5 + 5x+2 = 3x + 3x +1 + 3x+2 18. (x + 1) x-3 = 1 Bµi III: Gi¶i c¸c ph-¬ng tr×nh: 19. 3x + 4 x = 5x 20. 3x + x - 4 = 0 21. x 2 - (3 - 2 x )x + 2(1 - 2 x ) = 0 22. 22x-1 + 32x + 52x+1 = 2 x + 3x+1 + 5x+2 Bµi IV: Gi¶i c¸c hÖ ph-¬ng tr×nh: ì4 x + y = 128 ï 23. í 3x -2y -3 =1 ï5 î ì5x+ y = 125 ï 24. í (x -y)2 -1 =1 ï4 î 1
- 2. http://www.mathvn.com ì32x - 2 y = 77 ï 25. í x y ï3 - 2 = 7 î ì2 x + 2 y = 12 26. í îx + y = 5 x-y ì x -y 2 - m 4 = m2 - m ïm 27. í víi m, n > 1. x+y x+y ï 3 - n 6 = n2 - n în Bµi V: Gi¶i vµ biÖn luËn ph-¬ng tr×nh: 28. (m - 2).2 x + m.2 - x + m = 0 . 29. m.3x + m.3- x = 8 Bµi VI: T×m m ®Ó ph-¬ng tr×nh cã nghiÖm: 30. (m - 4).9 x - 2(m - 2).3x + m - 1 = 0 Bµi VII: Gi¶i c¸c bÊt ph-¬ng tr×nh sau: 31. 9 32. 2 x 6 x +2 <3 1 2x -1 ³ 1 3x +1 2 x2 - x 33. 1 < 5 < 25 2 34. (x - x + 1)x < 1 2 35. (x + 2x 36. (x 2 - 1)x x -1 + 3) x+1 2 + 2x <1 > x2 - 1 3 Bµi VIII: Gi¶i c¸c bÊt ph-¬ng tr×nh sau: 37. 3x + 9.3- x - 10 < 0 38. 5.4 x + 2.25x - 7.10 x £ 0 1 3 - 1 1 - 3x 40. 52 x + 5 < 5 x +1 + 5 x 41. 25.2 x - 10 x + 5x > 25 39. 1 x +1 ³ 42. 9 x - 3x+2 > 3x - 9 21-x + 1 - 2 x 43. £0 2x - 1 Bµi IX: Cho bÊt ph-¬ng tr×nh: 4 x-1 - m.(2 x + 1) > 0 44. Gi¶i bÊt ph-¬ng tr×nh khi m= 16 . 9 2
- 3. http://www.mathvn.com 45. §Þnh m ®Ó bÊt ph-¬ng tr×nh tháa "x Î R . Bµi X: 2 æ 1 öx 1 +2 æ 1 öx è3ø è3ø 46. Gi¶i bÊt ph-¬ng tr×nh: ç ÷ + 9. ç ÷ > 12 (*) 47. §Þnh m ®Ó mäi nghiÖm cña (*) ®Òu lµ nghiÖm cña bÊt ph-¬ng tr×nh: 2x 2 + ( m + 2 ) x + 2 - 3m < 0 Bµi XI: Gi¶i c¸c ph-¬ng tr×nh: 48. log5 x = log5 ( x + 6 ) - log5 ( x + 2 ) 49. log5 x + log25 x = log 0,2 3 ( ) 50. log x 2x 2 - 5x + 4 = 2 51. lg(x 2 + 2x - 3) + lg 52. x+3 =0 x -1 1 .lg(5x - 4) + lg x + 1 = 2 + lg 0,18 2 Bµi XII: Gi¶i c¸c ph-¬ng tr×nh sau: 53. 1 2 + =1 4 - lg x 2 + lg x 54. log 2 x + 10 log 2 x + 6 = 0 55. log 0,04 x + 1 + log 0,2 x + 3 = 1 56. 3log x 16 - 4 log16 x = 2 log 2 x 57. log x2 16 + log2x 64 = 3 58. lg(lg x) + lg(lg x 3 - 2) = 0 Bµi XIII: Gi¶i c¸c ph-¬ng tr×nh sau: æ è 59. log3 ç log9 x + ( (4 1 ö + 9 x ÷ = 2x 2 ø ) ( + 4 ) .log ( 4 ) 60. log 2 4.3x - 6 - log 2 9 x - 6 = 1 61. log2 x +1 2 ( ) x ) + 1 = log 1 2 1 8 62. lg 6.5x + 25.20 x = x + lg25 ( 63. 2 ( lg 2 - 1) + lg 5 ( ) x ) ( + 1 = lg 51- x +5 ) 64. x + lg 4 - 5x = x lg 2 + lg3 65. 5lg x = 50 - x lg5 3
- 4. http://www.mathvn.com 66. x - 1 log 2 lg2 x -lg x2 x = x -1 3 log x 67. 3 3 + x 3 = 162 Bµi XIV: Gi¶i c¸c ph-¬ng tr×nh: ( ) 68. x + lg x 2 - x - 6 = 4 + lg ( x + 2 ) 69. log3 ( x + 1) + log5 ( 2x + 1) = 2 70. ( x + 2 ) log32 ( x + 1) + 4 ( x + 1) log3 ( x + 1) - 16 = 0 log ( x +3 ) 71. 2 5 =x Bµi XV: Gi¶i c¸c hÖ ph-¬ng tr×nh: ìlg x + lg y = 1 72. í 2 2 îx + y = 29 ìlog3 x + log3 y = 1 + log3 2 73. í îx + y = 5 ( ) ìlg x 2 + y 2 = 1 + 3lg2 ï 74. í ïlg ( x + y ) - lg ( x - y ) = lg3 î ìlog 4 x - log 2 y = 0 ï 2 2 ïx - 5y + 4 = 0 î 75. í ì x+y ï y x = 32 76. í 4 ïlog3 ( x + y ) = 1 - log3 ( x + y ) î ìlog x xy = log y x 2 ï 77. í 2 log x ïy y = 4y + 3 î Bµi XVI: Gi¶i vµ biÖn luËn c¸c ph-¬ng tr×nh: 78. lg é mx 2 + ( 2m - 3 ) x + m - 3ù = lg ( 2 - x ) ë û 79. log3 a + log x a = log x a 3 80. logsin x 2.logsin2 x a = -1 81. log a.log2 a x a2 - 4 =1 2a - x Bµi XVII: T×m m ®Ó ph-¬ng tr×nh cã nghiÖm duy nhÊt: ( ) 82. log3 x 2 + 4ax + log 1 ( 2x - 2a - 1) = 0 3 4
- 5. http://www.mathvn.com 83. lg ( ax ) =2 lg ( x + 1) Bµi XVIII: T×m a ®Ó ph-¬ng tr×nh cã 4 nghiÖm ph©n biÖt. 2 84. 2 log3 x - log3 x + a = 0 Bµi XIX: Gi¶i bÊt ph-¬ng tr×nh: ( ) 85. log8 x 2 - 4x + 3 £ 1 86. log3 x - log3 x - 3 < 0 ( )û 87. log 1 é log 4 x 2 - 5 ù > 0 3 ë ( ) 88. log 1 x 2 - 6x + 8 + 2 log5 ( x - 4 ) < 0 5 89. log 1 x + 3 5 ³ log x 3 2 ( ) 90. log x é log9 3x - 9 ù < 1 ë û 91. log x 2.log2x 2.log 2 4x > 1 4x + 6 92. log 1 ³0 x 3 93. log2 ( x + 3 ) ³ 1 + log2 ( x - 1) 94. 2 log8 (x - 2) + log 1 (x - 3) > 8 æ ç è 2 3 ö ÷ 2 ø 3x + 4.log x 5 > 1 95. log3 ç log 1 x ÷ ³ 0 96. log5 x 2 - 4x + 3 ³0 x2 + x - 5 98. log 1 x + log3 x > 1 97. log3 2 ( ) 99. log 2x x 2 - 5x + 6 < 1 100. log3x -x2 ( 3 - x ) > 1 101. log æ 2 5 ö ç x - x + 1÷ ³ 0 2 è ø x2 +1 3x 5
- 6. http://www.mathvn.com 102. x -1 ö æ log x+6 ç log 2 ÷>0 x+2ø 3 è 103. log2 x + log2 x £ 0 2 104. log x 2.log x 2 > 16 1 log 2 x - 6 105. 2 log3 x - 4 log3 x + 9 ³ 2 log3 x - 3 106. log2 x + 4 log2 x < 2 4 - log16 x 4 1 ( ) 2 Bµi XX: Gi¶i c¸c bÊt ph-¬ng tr×nh: 107. 108. 109. 110. 2 6 log6 x + x log6 x £ 12 3 1 x 2-log2 2x-log2 x > x x log 2 2 - 1 .log 1 2 x +1 - 2 > -2 ( ( ) ( 2 ) ) ( 2 log5 x 2 - 4x - 11 - log11 x 2 - 4x - 11 ) 3 2 - 5x - 3x 2 ³0 Bµi XXI: Gi¶i hÖ bÊt ph-¬ng tr×nh: 111. ì x2 + 4 >0 ï 2 í x - 16x + 64 ïlg x + 7 > lg(x - 5) - 2 lg2 î ( ) ( ) ì( x - 1) lg2 + lg 2 x+1 + 1 < lg 7.2 x + 12 ï 112. í ïlog x ( x + 2 ) > 2 î ìlog2 -x ( 2 - y ) > 0 ï 113. í ïlog 4-y ( 2x - 2 ) > 0 î Bµi XXII: Gi¶i vµ biÖ luËn c¸c bÊt ph-¬ng tr×nh( 0 < a ¹ 1 ): 114. x loga x +1 > a 2 x 1 + log 2 x a 115. >1 1 + log a x 1 2 116. + <1 5 - log a x 1 + loga x 1 117. log x 100 - loga 100 > 0 2 Bµi XXIII: 6
- 7. http://www.mathvn.com 118. ( ) ( Gi¶i bÊt ph-¬ng tr×nh ®ã. Bµi XXIV: T×m m ®Ó hÖ bÊt ph-¬ng tr×nh cã nghiÖm: 119. ) Cho bÊt ph-¬ng tr×nh loga x 2 - x - 2 > loga - x 2 + 2x + 3 cã nghiÖm x = 9 . 4 ìlg 2 x - m lg x + m + 3 £ 0 í îx > 1 Bµi XXV: Cho bÊt ph-¬ng tr×nh: x 2 - ( m + 3 ) x + 3m < ( x - m ) log 1 x 2 120. Gi¶i bÊt ph-¬ng tr×nh khi m = 2. 121. Gi¶i vµ biÖn luËn bÊt ph-¬ng tr×nh. Bµi XXVI: Gi¶i vµ biÖn luËn bÊt ph-¬ng tr×nh: 122. ( ) loga 1 - 8a - x ³ 2 (1 - x ) 7
- 8. http://www.mathvn.com Bµi tËp ph-¬ng tr×nh, bÊt ph-¬ng tr×nh mò vµ logarit – phÇn 2 1. 2. 3. 4. 5. 2 x .3 x -1.5 x -2 = 12 log 2 log 2 x = log 3 log 3 x log 2 log 3 log 4 x = log 4 log 3 log 2 x log 2 log 3 x + log 3 log 2 x = log 3 log 3 x log 2 log x 3 ³ log 3 log x 2 x log2 ( 4 x ) ³ 8 x 2 2 2 7. x lg x -3 lg x -4,5 = 10 -2 lg x 8. x log x +1 ( x -1) + ( x - 1) log x +1 x £ 2 9. 5 lg x = 50 - x lg 5 log 2 x log x 10. 6 6 + x 6 £ 12 log ( x +3 ) 11. 2 5 =x log 2 x log x 12. 3 3 + x 3 = 162 6. 13. 14. 15. 16. 17. 18. 19. 20. 21. x x +2 = 36.32- x 1 1 > x +2 2 3 x +5 x - 6 3 1 1 ³ 3 x +1 - 1 1 - 3 x 8 2 1 2 x -1 1<5 ³2 x 2 -x 1 3 x +1 < 25 æ5 2 ö (0,08) ³ç ç 2 ÷ ÷ è ø log 2 x + log 2 x 8 £ 4 5 2 log 5 x + log 5 x = 1 x log 5 5 x 2 . log 2 5 = 1 x log x - 0 , 5 (2 x -1 ) log x - 0 , 5 x ( ) log x 5 x = - log x 5 23. log sin x 4. log sin 2 x 2 = 4 22. 24. log cos x 4. log cos2 x 2 = 1 8
- 9. http://www.mathvn.com 25. log 2 ( x +1) 4( x + 1) + 2 log x +1 ( x + 1) = 5 2 26. log 3 x - log 3 x - 3 < 0 [ )] ( log1 / 3 log 4 x 2 - 5 > 0 28. log1 / 3 x + 5 / 2 ³ log x 3 29. log x 2. log 2 x 2. log 2 4 x > 1 27. 30. log 3 x2 - 4x + 3 x2 + x - 5 ³0 x -1 ö æ log x +6 ç log 2 ÷>0 x + 2ø 3 è 1 32. log x 2. log x / 16 2 > log 2 x - 6 33. log x 2 2 x ³ 1 31. ( ) log x log 9 3 x - 9 £ 1 3x + 2 35. log x >1 x+2 36. log 3 x - x 2 (3 - x ) > 1 34. ( [ ) )] log x 5 x 2 - 8 x + 3 > 2 x 38. log x log 3 9 - 6 = 1 39. 3 log x 16 - 4 log16 x = 2 log 2 x 40. log x 2 16 + log 2 x 64 = 3 37. 41. ( 1 log1 / 3 2 x 2 - 3 x + 1 1 + log 2 x a 42. >1 1 + log a x 43. ( > 1 log1 / 3 ( x + 1) (0 < a ¹ 1) ) log a 35 - x 3 > 3 víi 0 < a ¹ 1 log a (5 - x ) 2 sin x -2 cos x +1 æ1ö -ç ÷ è 10 ø cos x -sin x -lg 7 + 5 2 sin x -2 cos x +1 = 0 44. 2 45. log 5 x 2 - 4 x - 11 - log11 x 2 - 4 x - 11 ³0 2 - 5 x - 3x 2 ( ) 2 ( ) 3 9
- 10. ( http://www.mathvn.com ) ( ) 2 log 2+ 3 x 2 + 1 + x + log 2- 3 x 2 + 1 - x = 3 47. log 2 x + log 3 x + log 5 x = log 2 x log 3 x log 5 x 2 48. log1 / 5 ( x - 5) + 3 log 5 5 ( x - 5) + 6 log1 / 25 ( x - 5) + 2 £ 0 46. ( ) 49. Víi gi¸ trÞ nµo cña m th× bÊt ph-¬ng tr×nh log1 / 2 x - 2 x + m > -3 cã nghiÖm vµ mäi nghiÖm cña nã ®Òu kh«ng thuéc miÒn x¸c ®Þnh cña hµm sè ( 2 ) y = log x x 3 + 1 log x +1 x - 2 1 log m 100 > 0 2 ì( x - 1) lg 2 + lg(2 x +1 + 1) < lg(7.2 x + 12) 51. í îlog x ( x + 2 ) > 2 50. Gi¶i vµ biÖn luËn theo m: log x 100 - x 1 + 2 2 52. T×m tËp x¸c ®Þnh cña hµm sè y = æ- x 5ö log a ç + ÷ è 2 2ø 53. 2 log 3 x - 4 log 3 x + 9 ³ 2 log 3 x - 3 54. 2 log1 / 2 x + 4 log 2 x < 2 4 - log16 x 4 55. log 2 ( ( ) (0 < a ¹ 1) ) x 2 + 3 - x 2 - 1 + 2 log 2 x £ 0 5 x - 51- x + 4 = 0 3 x + 9.3- x - 10 < 0 x -1 x æ1ö æ1ö 58. ç ÷ - ç ÷ > 2 log 4 8 è4ø è 16 ø 56. 57. æ1ö 59. ç ÷ è3ø 2 x 2/ x æ1ö + 9.ç ÷ è3ø 2 +1 / x 3 x +3 x 8 -2 + 12 = 0 2 x 61. 5 + 5 < 5 x +1 + 5 60. 62. 63. 64. > 12 x 5 16 = 10 2 2 x + 2 -2 x + 2 x + 2 - x = 20 (5 + 24 ) + (5 - 24 ) (3 + 5 ) + 16(3 - 5 ) = 2 x x x x x +3 10
- 11. http://www.mathvn.com 65. 66. 67. (7 + 4 3 ) x ( ) x -3 2- 3 +2 = 0 ( 7 - 4 3 ) + ( 7 + 4 3 ) ³ 14 ( 2 - 3) + ( 2 + 3) = 4 x x x x (5 + 2 6 ) ( tan x ) + 5-2 6 1/ x 1/ x 69. 4 + 6 = 91 / x x x x 70. 6.9 - 13.6 + 6.4 = 10 x x x 71. 5.4 + 2.25 - 7.10 £ 0 68. 72. 3 x tan x x = 10 4 - 15 + 4 + 15 ³ 8 2 2 +1 x 3 2 - 34.15 2 x - x + 25 2 x - x +1 ³ 0 3 sin 2 x - 2 sin x 74. log 7- x 2 = log 7- x 2 2 sin 2 x cos x 2 75. log x +3 3 - 1 - 2 x + x = 1 / 2 76. log x 2 (2 + x ) + log 2 + x x = 2 73. 92 x-x 3 ( ) 1 77. log 2 (3 x - 1) + 78. log 2 4 x + 4 = x - log 1 2 x +1 - 3 ( (9 ) x +1 log ( x + 3 ) 2 = 2 + log 2 ( x + 1) ( ) 2 ) log 3 - 4.3 - 2 = 3 x + 1 80. 1 + log 2 ( x - 1) = log x -1 4 79. 81. 82. 83. x ( ) ( ) log (2 - 1) log (2 - 2 ) > -2 ( 5 + 2) ³ ( 5 - 2) log 2 4 x +1 + 4 . log 2 4 x + 1 = log1 / 2 1 8 x +1 x 2 1/ 2 x -1 x +1 x -1 21- x - 2 x + 1 84. £0 2x - 1 x x æ ö æ ö 85. log 3 ç sin - sin x ÷ + log 1 ç sin + cos 2 x ÷ = 0 2 2 è ø ø 3è 3 1 æ x -1ö 2 2 86. log 27 x - 5 x + 6 = log 3 ç ÷ + log 9 ( x - 3) 2 è 2 ø ( ) 11
- 12. http://www.mathvn.com 87. T×m m ®Ó tæng b×nh ph-¬ng c¸c nghiÖm cña ph-¬ng tr×nh ( ) ( ) 2 log 4 2 x 2 - x + 2 m - 4m 2 + log 1 x 2 + mx - 2 m 2 = 0 lín h¬n 1. 2 88. T×m c¸c gi¸ trÞ cña m ®Ó ph-¬ng tr×nh sau cã nghiÖm duy nhÊt: log 5 +2 x 2 + mx + m + 1 + log 5 -2 x = 0 . ( ) ( 89. T×m m ®Ó ph-¬ng tr×nh 2 log 4 2 x - x + 2 m - 4 m cã 2 nghiÖm u vµ v tho¶ m·n u2+v2>1 90. log cos x sin x ³ log sin 2 x cos x 93. 94. 95. 96. 97. 98. 2 ) + log (x 1/ 2 2 ) + mx - 2 m 2 = 0 x 15 + 1 = 4 x 91. 92. 2 x 2 2 = 3 +1 x 9 x = 5 x + 4 x + 2 20 2 2 x -1 + 32 x + 5 2 x +1 = 2 x + 3 x +1 + 5 x +2 x 1/ x æ5ö æ2ö ç ÷ + ç ÷ = 2,9 (*) è2ø è5ø 1 + 2 x +1 + 3 x +1 < 6 x 3 log 3 1 + x + 3 x = 2 log 2 x 2x + 1 2 x 2 - 6 x + 2 = log 2 ( x - 1)2 x ( 1- x 2 ) 1-2 x x -2 2x 2 x x 100. x - 3 - 2 x + 2 1 - 2 = 0 x x x 101. 25.2 - 10 + 5 > 25 x x x +1 102. 12.3 + 3.15 - 5 = 20 99. 2 x 2 -2 ( x2 = ) ( ) 103. log2x+2log7x=2+log2x.log7x 104. 2 log 3 cot x = log 2 cos x 105. log x ( x + 1) = lg 1,5 ìlog 2 1 + 3 sin x = log 3 (3 cos y ) ï ïlog 2 1 + 3 cos y = log 3 (3 sin x ) î 106. í ( ( ) ) ( ( ) ) ìlog 2 1 + 3 1 - x 2 = log 3 1 - y 2 + 2 ï 107. í ïlog 2 1 + 3 1 - y 2 = log 3 1 - x 2 + 2 î ( ) 108. lg x + x - 6 + x + x - 3 = lg( x + 3) + 3 x 2 2 12
- 13. http://www.mathvn.com 109. Chøng minh r»ng nghiÖm cña ph-¬ng tr×nh 2 log 6 ®¼ng thøc cos px 16p < sin . 16 x ( ) x + 4 x = log 4 x tho¶ m·n bÊt 110. T×m x sao cho bÊt ph-¬ng tr×nh sau ®©y ®-îc nghiÖm ®óng víi mäi a: ( ) log x a 2 - 4a + x + 1 > 0 2 111. x + lg x - x - 6 = 4 + lg( x + 2) 112. log 2 x + log 3 ( x + 1) = log 4 ( x + 2) + log 5 ( x + 3) ( ) 6 - 3 x +1 10 113. T×m nghiÖm d-¬ng cña bÊt ph-¬ng tr×nh > (*) x 2x - 1 ìlog x (6 x + 4 y ) = 2 114. í îlog y (6 y + 4 x ) = 2 ( ) x 2 + 3 - x 2 - 1 + 2 log 2 x £ 0 2 116. ( x + 2 ) log 3 ( x + 1) + 4( x + 1) log 3 ( x + 1) - 16 = 0 x -2 117. 3.25 + (3 x - 10)5 x -2 + 3 - x = 0 2 118. T×m a ®Ó ph-¬ng tr×nh sau cã 4 nghiÖm ph©n biÖt 2 log 3 x - log 3 x + a = 0 115. log 2 119. ( x + 1) log1 / 2 x + (2 x + 5 ) log1 / 2 x + 6 ³ 0 2 120. x - 8e 4 x -1 ( > x x 2 e x -1 - 8 1+ x 121. 4 x + 3 . x + 3 ) < 2.3 x . x 2 + 2 x + 6 2 2 122. ln (2 x - 3) + ln 4 - x = ln (2 x - 3) + ln( 4 - x ) 2 ( x ( ) ) æ2 ö x 2 - 7 x + 12 ç - 1 ÷ £ èx ø ( 14 x - 2 x ) 2 x 124. Trong c¸c nghiÖm (x, y) cña bÊt ph-¬ng tr×nh log x 2 + y 2 ( x + y ) ³ 1 h·y t×m nghiÖm cã 123. 2 + 2 - 24 + 2 log x 2 - 5 x - 3 x 2 + 2 x > 2 x.3 x 2 - 5 x - 3 x 2 + 4 x 2 .3 x . ét +1 2 ù 125. T×m t ®Ó bÊt ph-¬ng tr×nh sau nghiÖm ®óng víi mäi x: log 2 ê x + 3 ú > 1. ët + 2 û 2 126. T×m a ®Ó bÊt ph-¬ng tr×nh sau tho¶ m·n víi mäi x: log 1 x + 2 a > 0 . tæng x+2y lín nhÊt ( a +1 ( ) ) x 2 . log 2 a 2 + 2 x + log a 2 127. T×m a ®Ó bÊt ph-¬ng tr×nh sau nghiÖm ®óng víi mäi x: <1 2x - 3 - x2 13
- 14. http://www.mathvn.com æ1ö è3ø 2 x æ1ö è3ø 128. T×m m ®Ó mäi nghiÖm cña bÊt ph-¬ng tr×nh ç ÷ + 3ç ÷ cña bÊt ph-¬ng tr×nh (m-2)2x2-3(m-6)x-(m+1)<0. (*) 129. (3 + 5 ) + (3 - 5 ) 130. (3 + 2 2 ) = ( 2 - 1) + 3 2 x-x2 x 2 x-x2 1 +1 x > 12 còng lµ nghiÖm 2 - 21+2 x - x £ 0 x 2.3 x - 2 x +2 131. £1 3x - 2 x 2 2 2 x2 -x 132. 6.9 - 13.6 2 x - x + 6.4 2 x - x £ 0 2 133. log 2 x + 2 . log (2 -x ) 2 - 2 ³ 0 ( ) log 4 x 2 134. 4 2 - x 2 = 2.3 2 2 2 135. log 3 x +7 9 + 12 x + 4 x + log 2 x +3 6 x + 23 x + 21 = 4 log 2 x ( log 6 ) ( ) 14