ph-bpt mũ, lôgarit

Chuyên đề pt,bpt mũ –lôgarits GV: Lơng Thị Lan Phơng BÀI TẬP VỀ PHƯƠNG TRèNH MŨ Bài1: Giải cỏc phương trỡnh sau: 1... Chuyên đề pt,bpt mũ –lôgarits GV: Lơng Thị Lan Phơng9... Chuyên đề p

Trang 1

Chuyên đề pt,bpt mũ –lôgarits GV: Lơng Thị Lan Phơng

BÀI TẬP VỀ PHƯƠNG TRèNH MŨ

Bài1: Giải cỏc phương trỡnh sau:

1 9x+1 = 27 2x+2

2 3 2x+ 5 = 3x+ 2 + 2

3 2x− 1 + 2x− 2 + 2x− 3 = 448

4 3x− 1 2x2 = 8 4x− 2

5 2x 5x = 0 , 2 ( 10x−1 ) 5

6 ( 2 + 3 ) 2x+ 3 = 2 − 3

7 2x2− 3x− 2 =41

8 2 3x+ 1 − 6 3x− 1 − 3x = 9

9 2x+ 1 5x = 200

10 0 , 125 4 2x− 3 = ( 4 2 )x

11.3x+1+ 18 3 −x = 29

12 27x+ 12x = 2 8x

13 3 4x = 4 3x

14 3 .8x+ 1 =36

x

15 x6 5−logx5 = 5−5

16 6x+ 6x+1 = 2x+ 2x+1 + 2x+2

1

9 6

4

1

= + −

−

18 2 sin2x + 4 2 cos2x = 6

1 2 cos 1 2

cos

2

17 7

5

128 25 0

+

−

+

x x

x

21 4x − 3x−0 , 5 = 3x+0 , 5 − 2 2x−1

22 5x−1 = 10x 2−x 5x+1

23 3 4x+ 8 − 4 3 2x+ 5 + 28 = 2 log2 2

Bài 2: Giải phương trỡnh sau:

1.(3 − 2 2)3x = 3 + 2 2

2 5x+ 1 + 6 5x − 3 5x− 1 = 52

3 3x+1 + 3x+2 + 3x+3 = 9 5x + 5x+1 + 5x+2

4 3x 2x+1 = 72

x

2 1

125

25

1

=











6 ( 0 , 5 ) 2 + 3x = ( 2 ) −x

7 4x+ 1 − 6 2x+ 1 + 8 = 0

8 3 1 +x + 3 1 −x = 10

9 3 25x + 2 49x = 5 35x

10 32x+4+ 45 6x − 9 22x+2 = 0

11 8x+ 1 + 8 ( 0 , 5 ) 3x + 3 2x+ 3 = 125 − 24 ( 0 , 5 )x

12 ( 6 + 35) (x+ 6 − 35)x= 12

13 5 7x = 7 5x

14 5 .8 x−1 =500

x x

15 5 3 − log 5x = 25x

16 x−6 3−logx3 = 3−5

17 9xlog9x =x2

18 x4 5 3 = 5 logx5

19 2x2−4 = 3x−2

20 4log0 , 5(sin2x+5sinx.cosx+2) =91

21* 3x = 5 − 2x

5

− +

−

=











23* 6x+ 8x= 10x

24* ( 5 + 2 6) (x + 5 − 2 6)x = 10x

25*.( 2 − 3) (x+ 2 + 3)x= 2x

6

1 2

1 2 3

1











−













− +













x x x

x x

27.3 2x− 1 + 3x− 1 ( 3x− 7 ) −x+ 2 = 0

28 25 5 −x − 2 5 5 −x(x− 2 ) + 3 − 2x= 0

29* xlog29 = x2 3 log2x − xlog23

30* 3 4 5 2

x

31 2 cos2x + 4 2 sin2x = 6

32

0 5

15

1

8 log sin cos 1

cos 2 sin











+

x x x

x

Bài 3: Giải cỏc phương trỡnh sau:

1.5x2 − 3x2+1 = 2(5x2−1 − 3x2−2) ĐS:

3

;

x

5 10

10

8 125 , 0

+

−

+

x x

x

3.3x−1 = 18 2x 2−2x 3x+1

17 7

5 2187 9

1

+

−

+

x x

x

5 2x−1 − 3x = 3x−1 − 2x+2

6 7 3x + 9 5 2x= 5 2x + 9 7 3x

x x x

1 5 1

1 5

2 4

2

1













1 2

3

3 2 2

9x − x+ = x+ − x−

Trang 2

1 1

3

3 10 3

+

−

=

x x

x

10 2x 3x+1 = ( 3 )x+2

11 ( ) 2 2 24 9 2 12

5

3 5

.

6

,











x

x x

x

1 2 1 4 1

3 2 ) ( 4 ) 2

(

)

2

−

2

1 4 6 9

.

3

1

4

.

3 x + x+ = x+ − x+

14 2x + 2x−1 + 2x−2 = 3x + 3x−2 − 3x−1

15 x x =x 2x− 3

16 (x2 − 5x+ 4)x2−4= 1

17 (x+ 4 )x2− 5x+ 6 = 1

18 x3 2x = ( x)x

x x

− +











 +

=













+

1 2

1 5 2

1

2 1

2

20.(x2 − 2x+ 2 ) 9 −x2 = 3 x2 − 2x+ 2

21 (x2 −x + 1 ) 4 −x2 = x2 −x + 1

Bài4: Giải cỏc phương trỡnh sau:

1 3 2x2+6x−9 + 4 15x2+3x−5 = 3 5 2x2+6x−9

2 3x+ 2 + 9x+ 1 = 4

3.4x+ 3 + 2x+ 7 − 17 = 0

4 5 1 +x2 − 5 1 −x2 = 24

5 5 x − 5 3 − x − 20 = 0

6 4 x − 4 1 + x = 3 2x+ x

1 1

1

25 35

8 125x + 50x = 2 3x+1

9 2.49 2 9.14 2 7.4 2 0

= +

x

10 25 3.101 21 2 0

2

1

=

−

+

x x x

11 4x+ x2− 2 − 5 2x− 1 + x2− 2 = 0

12 4x− x2 − 5 −12.2x 1− x2−5 +8=0

13 3.2 8.2 2 4 0

1 1

1

= +

+

x

14 82 +23x+3 −20=0

x

15.3 2x+ 4 + 45 6x − 9 2 2x+ 2 = 0

16 22x 9x − 2 63x−1 + 42x−1 34x−2 = 0

17 8x + 18x = 2 27x

6

1 3 5 2

−

=











x

1 1

1

9 6

4

.

20 4 =92 +7

x x

21 22x − 3 2x+2+ 32 = 0

22 5 3x + 9 5x + 27 ( 5 − 3x + 5 −x) = 64

23 23x − 6 2x − 23(1−x) + 12 2 −x = 1

24 ( 2 + 3) (x+ 2 − 3)x= 4

25 ( 4 + 15 )x + ( 4 − 15 )x = 62

26 ( 2 + 3 )x + ( 7 + 4 3 )( 2 − 3 )x = 4 ( 2 + 3 )

27 ( 7 + 4 3 )x − 3 ( 2 − 3 )x = − 2

28 ( 3 + 5 )x + ( 3 − 5 )x= 7 2x

29 3 ( 1 + 5 )x − ( 5 − 1 )x = 2x+1

30 ( 7 + 4 3)cosx+( 7 − 4 3)sinx = 4

) 1 5 ( 3 2

) 5 1 ( + x−x + 1 +x−x = − x−x

32 3 25x + ( 3x− 10 ) 5x− 2 + 3 −x= 0

33 9x + 2 (x− 2 ) 3x + 2x− 5 = 0

34 x2 − ( 3 − 2x)x+ 2 ( 1 − 2x) = 0

Bài 5:Giải cỏc phương trỡnh sau:

1 2x+ 1 + 3x= 6x + 2

2 15x − 3 5x + 3x = 3

3 2x+ 1 + 3 2 2x = 6 + 2 3x

4 4x2 +x 3x+ 3x+ 1 = 2x2 3x+ 2x+ 6

5 2 2x2−5x+2 + 2 4x2−8x+3 = 1 + 2 6x2−13x+5

6 2x2−3x+3 + 2x−1 = 2 + 2 (x−1 ) 2

7 3 4x−3 + 3x−2 = 9 + 3 5x−7

8 5 3 − 2x2 + 5x2 +x− 1 = 5 + 5 1 +x− 2x2

9.x2 2x + 6x+ 12 = 6x2 +x 2x + 2x+1

10.x3 3x + 27x=x 3x+ 1 + 9x3

11.x2 2x+1 + 2x−3+2 =x2 2x−3+4 + 2x−1

12.( )7 x+1+ 7x2− 2 = 7x2+x− 4 + 7

Bài 6: Giải cỏc phương trỡnh sau.

1.5 .8 x−1 =500

x x

2.3x2− 4 = 3 25 125x

x

+

(

3 36 3 8

4 2x2− 2x 3x = 1 , 5

5 4x 6x = 2 9 2x

6 3 .8x+ 1 =36

x x

7 5 .2 1 4

3

x x

8 4tan4 = 1600 2

x

Trang 3

9 4 xtan x = 100

10 7 log252( 5x) − 1 = xlog57

x

2

1

3 2 + =

2 ( 4 + 15 )x + ( 4 − 15 )x = ( 2 2 )x

3 2010 sin2x − 2010 cos2x = cos 2x

x

4

7

9 2 + =

5 3 4 5 2

x

6 3x+ 4x+ 5x+ 14 = 8x

7.82 −32 −2x =39

x

8 2x+ 3x + 6x = ( 0 , 7 )x+1

9 15 2x + 4 7x = 23 , 5 10x − 6 5x − 4 3x

10 2 5 29 2

x x

11 ( 2 − 3 )x+ ( 2 + 3 )x= 4x

12 ( 3 − 2 )x+ ( 3 + 2 )x= ( 5 )x

13 x2 − ( 3 − 2x)x+ 2 ( 1 − 2x) = 0

14 x 2x =x( 3 −x) + 2 ( 2x − 1 )

15 3 25x− 2 − ( 3x− 10 ) 5x− 2 + 3 −x= 0

16.9x + 2 (x− 2 ) 3x + 2x− 5 = 0

17 2x+ 3x+ 5x = 10x

18 ( 3 + 5 ) 2x + 7 ( 3 − 5 ) 2x = 2 2x+3

19.2x− 1 − 2x2−x = (x− 1 ) 2

20 π sin x = cosx

**************************

BẤT PHƯƠNG TRèNH MŨ

Bài 8: Giải cỏc bất phương trỡnh sau:

1.2 3 − 6x > 1

2 2x+2 − 2x+3 − 2x+4 > 5x+1 − 5x+2

1

32

.

4

1

−

x x

x

4 9x < 2 3x+ 3

5.5 2x+ 1 > 5x + 4

6 2x+ 2 −x+ 1 − 3 < 0

2

1

( x2− 5x+ 4 >

8 6 2x+3 < 2x+7 3 3x−1

9 9x < 3x+ 1 + 4

10 3x − 3 −x+ 2 + 8 > 0

11 xlog3x+4 < 243

12 15 2x+3 > 5 3x+1 3x+5

1.( 4x2 + 2x+ 1 )x2−x > 1

2 2x + 2x+1 ≤ 3x + 3x−1

1

1 ( 5 2 ) )

2 5

−

x x

4 ( 2 + 1 ) +1 ≥ ( 2 − 1 )x− 1

x x

1 1

3

3 10 3

+

−

<

x x

x

3

1

3 2

−











≥

x x x

x

2 2

1

3

−

+

−

>

+

x x

x

x x x

x

8 − 12x2−7x+3 < 1

x

9 3x2+2 + 3x2 ≤ 2 5x2+1

3

1 3

1

3 72  >





















11 2log 3x2.5log 3x <400

12 (x+ 3 )x2− 5x+ 6 > 1

13 (x2 − 8x+ 16)x−6< 1

14 3 logx+ 2 < 3 logx2+ 5 − 2

15 log .log 1

1

<

x

x x

16 x2 logx ≥ 10x

9 6

8x ≥ x−

18 x −x + −x











<











2

1 2

19 2 2x− 1 + 2 2x− 3 − 2 2x− 5 > 2 7 −x + 2 5 −x − 2 3 −x

20 2 49x2 − 9 14x2 + 7 4x2 ≥ 0

21.25 2x−x2 + 1 + 9 2x−x2 + 1 ≥ 34 15 2x−x2

22 5 2x−10−3 x−2 − 4 5x−5 < 5 1+3 x−2

23 4x2−1 + 2 2x2−6 > 52 + 4x2−2

24 3x+1−22x+1−122x <0

25

3

2 4 5 12 5

5 7 4 1

+

−

x

26 8 3 x+4x + 91+4x ≥ 9 x

27 3 2x − 8 3x+ x+ 4 − 9 9 x+ 4 > 0

1 2

2 1

≤

−

+

−

x

x x

29 9x − 3x + 2 > 3x− 9

Trang 4

30 13x− 5 ≤ 2 ( 13x + 12 ) − 13x + 5

31 5x + 3 ≥ 2 ( 5x+ 4 ) − 5x− 3

32 ( 26 + 15 3 )x + 2 ( 7 + 4 3 )x − 2 ( 2 − 3 )x < 1

Bài 10: Giải cỏc bất phương trỡnh sau

1.4x2 +x +21 −x2 ≥2(x+ 1 ) 2 +1

2 4x2 +x 3 x + 3 1 + x≤ 2x2 3 x + 2x+ 6

3 4x+ 8 2 −x2 > 4 + (x2 −x) 2x+x 2x+ 1 2 −x2

4 2 − 5x− 3x2 + 2x> 2x3x 2 − 5x− 3x2 + 4x2 3x

5 2x+1+ 3x+1< 6x − 1

6

10

29 5

2

5 1 >











+











2

4

2

3

3 2

≥

−

+

−

x

3

2

3

.

5

2

1

<

−

+

x

PHƯƠNG TRèNH LễGARIT

1.log 1 log ( 2 1 )

2 1

2 = x −x−

x

2.log4(x+ 12 ) logx2 = 1

log 2

4 2

log

6

2 2

= +

x x

4 log3( 3x + 8 ) = 2 +x

5.log2x(x− 1 ) = 1

6 log2x+ log2(x− 1 ) = 1

7 log log log 3

2 1 4

2 x+ x=

8 log 3 x log3 x log9 x= 8

9 log 2x3 − 20 log x+ 1 = 0

10 loglog 2x x loglog 48x x

16

8 4

11.log9x27 − log3x3 + log9243 = 0

12 3 2 − log 3x = 81x

13 log2x= 3 −x

14 log2( 3 −x) + log2( 1 −x) = 3

2 ( 9 2 ) 10

16 log ( 3 1 ) log ( 3 1 3 ) 12

3

3 x − x+ − =

17 logx−14 = 1 + log2(x− 1 )

2

2 ( ) log log

=

+

2

1 log 2

1

3 3

20.4 lnx+ 1 − 6 lnx − 2 3 lnx2+ 2 = 0

21 3 log2x − log28x+ 1 = 0

8 log ) 4 (

2

23.log (log 2 3 log0,5 5 ) 2

5 , 0

24.log2( 4 3x − 6 ) − log2( 9x − 6 ) = 1

2

1 ) 1 2 log(

2

1

3

1 ) 2 ( log 6

1

8 1

2 x− − = x−

Bài 12: Giải cỏc phương trỡnh sau

1 log3x(x+ 2 ) = 1

2 log3x+ log3(x+ 2 ) = 1

3 log ( 2 3 ) log2( 6 10 ) 1 0

2 x − − x− + =

4 log ( 2x+ 1 − 5 ) =x

2

5 2 log 2x= log(x2 + 75 )

2

1 ) 10 log(x+ + x2 = −

7 log22(x− 1 )2+ log2(x− 1 )3= 7

8 log4x8 − log2x2 + log9243 = 0

9 3 log3x− log33x− 1 = 0

10 4 log9x+ logx3 = 3

6

7 log 3 logx − 4x+ =

81

27 9

3

log 1

log 1 log 1

log 1

+

= +

+

13 log ( 2 5 ) log 4 3

5 2

2

2 x − + x2− =

14.log9(log3x) + log3(log9x) = 3 = log34

15 log2 x log4 x log8x log16x =32

2

4

5 log 2 6 log log

17 5 3 − log 5x = 25x

18 x−6 3−logx3 = 3−5

19 4log0 , 5(sin2x+5sinx.cosx+2) =91

20 log 5 23

2

1 x= x−

21 x log(x 2x 1 ) logx

2

1 ) 1

Trang 5

22 log ( 3 2 ) log 2 3 1

3

10 log )

1 3

24 x+ log5( 125 − 5x) = 25

25 2 log3cotx= log2cosx

26 log2x− log4(x− 3 ) = 2

x

x x

2 log log

log

.

log

125 5

25

) 3 ( log

) 4 ( log 2 ) 3

(

log

1

2 4 1

6

= +

− +

x x

29 7 logx +xlog 7 = 98

1.log ( 3 2 2 1 ) 21

x

2 log ( 2 4 7 ) 2

2 x − x+ =

3 logx( 2x2 − 3x− 4 ) = 2

4 logx( 2x2 − 4x+ 3 ) = 2

3 2 2 8

2+ + + + x − x =

x x x

x

6 log ( 9 16 ) 2 log (31 4 2)

2

4 4

3 − x2 − x = + − x

7 log ( 4 1 ) log ( 2 3 6 )

2

2 x + =x+ x+ −

8

) 1 (

log ) 1 (

log

) 1 (

log ) 1 (

log

2 4 2 2

4

2

2 2

2

+

− +

+ +

=

= +

− +

+ +

x x x

x

x x x

x

9.log (2 54) log ( 3) 2log9( 4)

3 1

2

10 2log2x+log 2 x+log21x=9

11 log 3log log 2

2 1 2

2

2x+ x+ x=

12 log 2 log5 5 1

x

2 1 2 2 log

14 3xlog3x+ 2 = 4x+ log27x

15 log 5 log 5

1

1 3

5

+

−

x x

16

2 log 3 log 2 ) 6 log(

) 1 3 3 log(

3

1 36 log

+ +

+

=

= + + + +

−

x

x x x x

) 4 5

log(

log

−

x

3 1 3

3x+ x+ x=

4 2 log ) 2 1 ( log

2 1

) 1 log(

1

2 )

1 ( log 1

) 1 log(

1

− +

+

− +

−

+

x x

x

21

x x

x x x

2

) 3 2 5 ( log 3 2 5 log 2

2 6 1

2 6 2

+

=

−

22 4 − logx= 3 logx

23 x(log 5 − 1 ) = log( 2x+1)-log6

24 (log log 2 ) log( 1 2 ) log 6 2

1

= +

+

x

25 log ( 2) log 2 1 0

3 1

3 x− + x− =

26

2

11 log

log log2x+ 4x+ 8x=

27 log ( 2) 2 6log 3 5

8 1

2 x− = + x−

28 log ( 4 ) log ( 2 4 )

6 4

2

3+ x − = − x −

x x

x

1

) 1 (

log

) 1 (

log ).

1 (

log

2 6

2 2

−

=

− +

−

x x

x x x

x

2.log2x+ log3x= 1

3 log5x+ log3x= log 15

6

7 log 2 logx − 4x+ =

5

4 log 1 log log 2

x x

6 log 2 14log16 3 40log4 0

2

= +

x

7 log4(log2x) + log2(log4x) = 2

8 log2(log3x) = log3(log2 x)

1 log2( x − 1 ) = log5x

3 2

2 3 4

8+ x − x− = + x − x−

3 log (x2 x 8 ) log33x

4 log3( 5 + 3 x) = log2( x − 4 )

2 ( 1 ) log

Bài 16: Giải cỏc phương trỡnh sau:

Trang 6

1.(x− 2 )[log2(x− 3 ) + log3(x− 2 )]=x− 1

2.log ( 1 5 5 ) log ( 2 5 7 ) 2

3

2

2 + x − x+ + x − x+ =

********************************

BẤT PHƯƠNG TRèNH LễGARIT

1 log5( 3x− 1 ) < 1

2 log31(5x−1)>0

5

,

0 x − x+ ≥ −

4 log31−2 ≤ 0

x

5 log 2 log0,5 2 0

5

,

0 x+ x− ≤

6 log ( 2 2 ) log0,1( 3 )

1

,

0 x +x− > x+

7 log ( 2 6 5) 2log3(2 ) 0

3

1 x − x+ + −x ≥

8 11 loglog 21

2

4 ≤

−

x

9 log (6 1 36 ) 2

5

1 x+ − x ≥

10 log ( 2 6 18) 2log5( 4) 0

5

1 x − x+ + x− <

11 log21(5x+1)> −5

1

3

1

−

+

x

13 log ( 2 1 ) log0,8( 2 5 )

8

,

0 x +x+ > x+

1

2 1 (log

3

+

x x

15 xlog3x+4< 243

16 log 2 log24 4 0

2x+ x− ≥

17 log 3 log 3 0

3

<

− x

x

18 log2(x+ 4 )(x+ 2 ) ≤ 6

1

1 3 log

log2 4 2 >

+

− +

x

x x

20













−













<













−











4

1 log 1 2

1

log

3

1 3

1

x x

21 3 logx4 + 2 log4x4 + 3 log16x4 ≤ 0

1

1 (log log ) 1

1 (log

log

3

1 4 1 3

+

<

+

−

x

x x

x

23.log4 x− 3 < 1

24 log2x+ log3x< 1 + log3x log2x

2 log

2 log log

≠

>

−

+

x

a a

1 1

3 2 log

1

3 1 2

3

1 x − x+ > x+

2.log2x64 + logx216 ≥ 3

3 log ( 1 1) 1 loglog( 2( 3)1)

2

2 2

+

>

+ +

x x

x

4 log ( 1) log5(2 ) 5

5 logx( 3 − 2x) > 1

2 8

3 log > −

− x

x

7 log 2 2 3 ≤21

−

x

8 log (2 ) 8log (2 ) 5

4 1

2

2 −x − −x ≥

9 2 log7 x− log 7 x> 4

10 3 log 3 4 log4 2

2 x− x>

11 log3 x− 2 log9x> 2

1

1 3 (log log

4

1 3 1 4

+

≤ +

−

x

x x

x

13 log log2( 4x − 6 ) ≥ 1

x

14 log log3 3 0

3

2 x− ≥

3

1 2 log

2

+

−

x

3

1 2 log

2

+

−

x

*******************

PT-BPT MŨ LễGARIT QUA ĐỀ THI ĐẠI HỌC 1.(A-08)

4 ) 1 2 ( log ) 1 2

(

1

2 1

2x− x +x− + x+ x− =

Đs;x =2;x=5/4

2.(B-08)

4 (log log0,7 6 2 <

+

x

x x

Đs: -4<x<-3; x>8

3.(D-08)

Trang 7

log 3 2 0

2 2

x

x x

ĐS:2 − 2 ≤x< 1 ; 2 <x≤ 2 + 2

4.(A-07)

2log (4 3) log (2 3) 2

3 1

4

3

≤

<x

5.(B-07)

( 2 − 1) (x + 2 + 1)x − 2 2 = 0

ĐSx=1; x=-1

6.(D-07)

0 3 2 4

1 log ) 27 2

.

15

4

(

− +

+

x

Đs: Pt vụ nghiệm

7 (A-06)

0 27 2 18 12

.

4

8

.

3 x + x − x − x =

Đs:x=1

8.(B-06)

) 1 2 ( log 1 2 log 4 )

144

4

(

5 5

5 x + − < + x− +

Đs: 2<x<4

9.(D-06)

0 4 2 2

.

4

2x2+x − x2−x − 2x+ =

ĐS: x=0;x=1

10.(D-03)

2x2−x − 2 2 +x−x2 = 3

ĐS:x=-1;x=2

11.(B-02)

log (log3( 9x − 72 )) ≤ 1

x

ĐS: log3( 6 2 ) <x≤ 2

12.(CĐ-08)

log 2 ( 1 ) 6 log2 1 2 0

2 x+ − x+ + =

13.(Luật HN-98)

( 7 + 4 3 ) cosx + ( 7 − 4 3 ) cosx = 4

3 log 3 ) 12 7 ( log ) 2 3

(

2

2 x + x+ + x + x+ = + 15

.(YHN-97)

log2x64 + logx216 ≥ 3

16.(SPHN-D-00)

3 2x − 8 3 x+ 4 +x − 9 9 x+ 4 = 0

2 2x2+ 1 − 9 2x2+x + 2 2x+ 2 = 0

18.(YHN-00)

2

12 2

1 2

6

23x − x − 3(x−1) + x =

log( 10 ) log( 10 ) log( 100 2)

3 2 6

4 x ≤ 3 2 x+x + 4 x+1

21.(HVBCVT-98)

3 1 23 1 12 2

x x

x+ − + <

22 (YHN-99)

2 2x + 3 3x > 6x − 1

23.(TCKT-01)

1 3

1 log log 2 2 3

1 2 log 2 3 1 2

3

≥





















+











 + x−

x

24 (Dược-01)

2 1 2

2

x

25.(YHN-01) log2( x2 + 3 −x2 − 1 ) + 2 log2x≤ 0

26 (HVQHQT-01)

2

2 3 log >

+

x

27 (ĐHNN-99)

1 − >

x

) 1 ( log 1 1 2

1 log

) 1 ( log 2

5 1 5

25 x− ≥ x− −  x− 29

) 2 3 2 ( log 1 ) 2 3 2 (

2

4 x + x+ + > x + x+ 30 (TCKT-99)

x

2 1 2

2

3 2 2 1

4

2 9 log 32 4 log

8 log

2

1 x − x+ ≥

32.( ĐHQGHN-A99)

1

1 8 log

2

+

+ +

x

x x

33.(BCVT-99)

Trang 8

log22+log24x=3

x

34.(YHN_99)

225 log 3 log log

log5x+ 3x= 5 9

35.(TSNT-99)

0 2 ) 1 4 4 ( log ) 1 5 6

(

3 1

2

1− x x − x+ − −x x − x+ − =

log2x− log4x= −67

3 8

2

4 ( 1 ) 2 log 4 log ( 4 )

ĐHQGHN_00)

log5x= log7(x+ 2 )

3 log 2

1 log

2

1 ) 6 5

(

9 x − x+ = x− + x− 40.

(AN-01)

) 1 ( log 2 2 log

1 )

1

3

(

3

+

x x

x

41.(SPVinh-A01)

) 1 (

log

) 1 (

log ).

1 (

log

2 20

2 5

2

4

−

=

− +

−

x x

x x x

x

log 2( 2 +x) + log 2+x x= 2

x

43.(KTQD-01)

4 ) 21 23 6

( log ) 9 12

4

(

log3x+7 x2+ x+ + 2x+3 x2+ x+ =

44.(D-10)

4 4 2

2 2

4 x+ x+ + x = + x+ + x+ x−

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