ff486 family and friends 4 nguyễn văn hiền thư viện tư liệu giáo dục

[r]

phơng trình, bất phơng trình Lôgarit 1

2

log (x x  7x12) 2 2 log2x316 2 3 log (9 ) 32  x   x

4 (§H§N-97) log (3.22 1)

x x

  

5 5

log ( 1) log

1

x x

x  

 6 3log3x log9x5

7 27

5

log log log

3

x x x

8 log (4.32 x 6) log (9 x6) 1 9

2

2 log xlog xlog

10.

1

5

1

log log ( 2)

3 x

 

 

 

 

11. (§H-A2002)

2

3

log x log x 1 2m1

a) Giải phơng trình m=2

b) m=? để phơng trình có no

[1;3 ]

 12. (C§SPHP-2004)

a)

2

2

2

1

log ( 1) log ( 4) log (3 )

2 x  x   x

b) log (3 x22x1) log ( x22 )x 13. (C§CNHN-2004) Tìm TXĐ

2

2

2

1

4log log

y x x x

x

 

      

 

14 (CĐKTKTI-2005) Tìm TXĐ

2

log ( 2)

y x  x

15 (C§BTre-2005)

1

log 16 log 64 3x

x

 

16 (§HQGHN-B2000) log5xlog (7 x2) 17 (§HBKHN-2000)

2

4

log (x1)  2 log 4 xlog (4x)

18 (§HH-A2000) log (9 ) 32 x

x  

19 (§HH-D2000)

2

2

log (x 1) log ( x1)

20 (§HYHN-2000) lg (4 x1)2lg (2 x1)325 21 (§HCT-D2000) log log (log2 2x) 1

22 (§HAG-D2000) log (log4 2x) log (log 4x) 2 23 (§HNT-A2000)

2

3

log (x  x 1) log x2x x

24. (§HTN-G2000)

1

1 lg x2 lg x 25. (§HCT-B2000)

2

2

(x1) log (x3) 2 m 2(x1) log (x3)m 1 a) Giải phơng trình với m=-1

b) m=? phơng trình có nghiệm [ 1;1] 26. (HVQHQT-A2000)

2 4

2 2

log (x  x 1) log ( x  x1) log ( x x 1) log ( x  x 1)

27. (DHSPVinh-D2000)

5 5

(x 1) log log (3x 3) log (11.3x 9)

    

28. (HVCNBCVT-2000)

2

9 3

1

log ( 6) log log | |

2

x

29. (DHCD-2000)

3 3

2

4

log log

3

x x

30. (§HKT-2000) log7xlog (3 x2) 31. (HVQY-2000)

2

2 3

log  [x  2(m1) ] logx   (2x m  2) 0

m=? ph-ơng trình có nghiệm

32. (ĐHCSND-G2000)

3

log (x1) ( x5) log (x1) 2 x 6

33. (C§CNHN-2000)

3

4

16

log xlog xlog x 5

34. (§HQGHN-A2001)

2 7

log x2log x 2 log logx x

35. (§HSPHN2-A2001) logxalogaxaloga x2 a0 36. (§HSPVinh-AB2001)

2 2

4 20

log (x x 1).log (x x 1) log ( x x 1)

37. (§HNNI-B2001) log (2x2 x) log 2x x2 38. (§HKTQD-2001)

2

3

log x (9 12 x4 ) logx  x (6x 23x21) 4

39. (§HTM-2001)

1

2

(m1) log (x 2) ( m5)log (x 2)m1 0

40. (§HC§-2001)

1

2

2

log (4x 4) x log (2x 3)

   

41. (§HAN-A2001)

2

( 3)

1

log (3 1) log ( 1)

logx

x x



    

42. (§HTS-2001)

2

2 2 4

2

(log log ) log (log log ) log

2

x

x x x x

x

   

43. (§HCT-D2001)

a) log (22 4) log (22 12)

x x x

    

b)

2

5

log  (x mx m 1) log 

m=? pt cã nghiƯm

44. (§HDLP§-D2001) log (2 x1) log 16 x1 45. (HVKTQS-2001)

2 2

2

2

log xlog x 3m(log x 3)

m=? phơng trình có nghiệm [32;)

46. (§HDLP§-A2001)

1

log (9x 4.3x 2) 3x

   

47. (ĐHDLĐĐô-AV2001) log [log (9x x 6)] 48. (ĐHSPTPHCM-A2001)

2

2

log log

4log 2x x 2.3 x

 

49. (DHYDTPHCM-2001)

2 2

4

2

2log (2x  x2m 4m ) log ( x mx 2m ) 0

m=? để phơng trình có nghiệm 2 x x  50. (ĐHCSND-2001)

2

16

2

logx x 14 log xx 40 log x x0 51. (§HQGHN-B96)

2 2

log 16.logx 15

x x x 

52. (HVKTQS-97)

2

6

10 10

log x x (sin 3x sin ) logx x x (sin )x

   

53. (§HYTB-98)

 2  

2 3

log x x log x x

       

54. (§HYHN-98) log (6 4x8 x) log x 55. (§HTM-97)

2

logx (5x 18x16) 2

56. (§HYHN-97) log 64 log 16 32x  x2  57. (§HBKHN-98)

2

3 1

3

1

log log log ( 3)

2

x  x  x  x

58. (§HH-98)

1

log ( )

4

x x 

59. (§HNT II-98) log2xlog3x 1 log log2x 3x 60. (§HNNIHN-98)

2

2 0,5

2xlog (x  4x4) (  x1) log (2 x) 61. (ĐHTLợi-97)

2

log (log | |)

e

x 

62. (§HXD-96)

2

1

log 2

2

x  x x  x 

63. (§HBKHN-97)

2

2

2

log ( 1) log ( 1)

0

3

x x

x x

  

  

64. (§HKTróc-97)

lg( 2) 2

lg lg

x x

x  

 

65. (§HVH-D2001) log [log (3x x9)] 1

66. (§H§L-AB2001) logx m (x21) log x m (x2 x 2)

m=? để phơng trình có nghiệm 67. (ĐHDLTL-A2001)

2

log (x ax1) 1

68. (§YHN-2001) log (2 x2 3 x21) 2log 2x0 69. (C§XD1-2001)

2

2

`2

log (x  x) log ( x3) 0 70. (V§HMëHN-2001)

2

1 5

5 25

log (x5) 3log (x5) 6log ( x5) 0 

71. (§HAG-D1)

2 log (2 ) 1x x 

72. (HVQHQT-D2001)

3

log

2

x x x

  

73. (§HDHN-2001)

2

1

2

(x1) log x(2x5) log x 6

74. (§HNNI-A2001)

2

1

log (log ) log (log ) log

2

a a x  a ax  a

75. (DHDLHV-B2000) log (4x2 x5) 1

76. (C§-A2000)

2

2

log (1 x x  4) 0

77. (§HTS-2000)

2

4 2

1

log ( 12) log ( 2) log | |

2

x  x  x  x 

78. (DHYTB-2000) log2xlog 42x 

79. (§HLHN-2000)

5 lg

5 0

2x

x x x 

 

  80. (§HSPTPHCM-A2000)

2

9

81. (§HSPHN-A2000)

2

2

log x  2x m 4 log (x 2x m ) 5

82. (§H-B2002) log [log (93 72)] x

x  

82. (§H-D2002)

3

1

2

4

2

x x x

x

y y

y



  



 

 

 

83. (§HTL-2000)

2 2

3 3

3

log log log

2

log 12 log log

3

x

x y y

y

x x y



  

  

   

 

84. (§HTCKT-2000)

8 log log

4

4

log log

y x

x y

x y

  

 

 

 

85. (§H§N-A2001)

log (6 )

log (6 )

x y

x y

y x

 

  

 

 

86. (§HH-AB2001)

2

log (x y) log (a x y)

x y a

   

 

 

 Với

a=? hệ phơng trình có nghiệm? 87. (§HCT-A2001)

2

3

2

2

log ( 1) log ( 1) log

log ( 5) logx x

x x

x x m

 

   

  

   

 

Víi m=? hệ phơng trình có nghiệm phân biệt

88. (§H-A2004)

1

4 2

1

log ( ) log

25

y x

y

x y



  

 

  



89. (§H-B2005)

2

9

1

3log (9 ) log

x y

x y

    

 

 

 

90. (C§SP-A2004)

2 2

4

log ( )

2log log

x y

x y

  

 

 

 

91. (C§SPBN-2004)

2

1

2

log ( 3) log ( 3)

0

x x

x

  

 

92. (C§SPKT-2004) log log5x 3xlog5xlog3x

93. (C§SPTPHCM-2005)

2

5

9

log (3 ) log (3 )

x y

x y x y

  

 

   

94. (CĐKTKTCThơ-A2005)

2

2

2

log (x 2x3) log ( x3) log ( x1)

95. (C§SPHN-2005)

2

1

log (3 1)

log (x 3 )x  x

96. (C§SPVP-2005)

4 2

2 0,5 2

2

32

log log 9log 4log

8

x

x x

x  

   

 

97. (C§KTKH§N-2005) log (3 x 4) log 2x1 2 98. (C§YTTH-2005)

2

0,5 16

log x4log x 2(4 log x )

99. (CĐSPQBình-2005)

2

2

log ( ) log ( )

2

x y x y

x y

   

 

 



100. (C§SPQNg·i-2005) 3

4 32

log ( ) log ( )

x y y x

x y x y





 



    