Phương trình, bất phương trình mũ và lôgarit dùng dạy thêm

PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH MŨ
Bài 1.
a)
2
x 3x 1
1
3
3
− +
 
=
 ÷
 
b)
x 1 x 2
2 2 36
+ −
+ =
c)
x 1 x 1 x
1 x
1
2 .4 . 16
8
+ −
−
<
d)
2
2x 3x
1

1
2
−
 
≥
 ÷
 
Bài 2.
a)
x
2x 3
2
0,125.4
8
−
−
 
=
 ÷
 
b)
( )
2x 1
7x
x 1
8 0,25. 2
−
+
=
c)

( ) ( )
x 3 x 1
x 1 x 3
5 2 5 2
− +
− +
+ > −
d)
( )
1
1
x 1
x 3
2 x
2 2 4
−
+
 
=
 
 
 
Bài 3.
a)
1 1
x x
x 2x 1
2 2
4 3 3 2
− +

−
− = −
b)
x x 1 x 2 x x 1 x 3
5 5 5 3 3 3
+ + + +
+ + ≤ + +
Bài 4.
a)
2
x 4 x 2
2 .5 1
− −
=
b)
2
x 2x
3
2
2
−
=
c)
2
2x 3
x 2
x
3 .4 18
−
−

=
d)
x
4 x
x 2
8 4.3
−
+
=
Bài 5.
a)
2x x 1
3 3.3 12
−
+ =
b)
x 1 x
3 3 4 0
−
+ − =
Bài 6.
a)
x 1 x 4 x 2
4 2 2 16
+ + +
+ < +
b)
2 2
x x 1 x x 2
9 10.3 1 0

+ − + −
− + ≥
Bài 7.
a)
( ) ( )
x x
2 1 2 1 2 2 0− + + − ==
b)
( ) ( )
x x
5 24 5 24 10− + + ≤
c)
x 2
5 x
1
2 9
4
−
−
 
= +
 ÷
 
d)
x
2
x 2
9 10 4
2 4
−

+
=
Bài 8.
a)
3x 1 2x x
2 7.2 7.2 2 0
+
− + − =
b)
x x
x x
27 27
8 9.2 64
8 2
+ + + =
c)
( ) ( )
x x
7 4 3 3 2 3 2 0+ − − + =
Bài 9.
a)
( ) ( )
x x
x 3
3 5 16 3 5 2
+
+ + − =
b)
2 2
2x 1 x x 2x 2

2 9.2 2 0
+ + +
− + ≥
c)
2 2 2
2x 6x 9 x 3x 5 2x 6x 9
3 4.15 3.5
+ − + − + −
+ =
Bài 10.
Phương trình, bất phương trình mũ, lôgarit
a)
x x 3x 1
125 50 2
+
+ =
b)
x x x
8 18 2.27+ <
c)
x x x x
3.8 4.12 18 2.27 0+ − − =
Bài 11.
a)
2 2 2
x 3x 2 x 6x 5 2x 3x 7
4 4 4 1
− + + + + +
+ = +
b)

2 2
x x x x 2x
2 4.2 2 4 0
+ −
− − + =
c)
( )
2
2
x 1
x 3x 3 x 1
2 2 2 2
−
− + −
+ = +
d)
2 2
x 5x 6 1 x 6 5x
2 2 2.2 1
− + − −
+ = +
Bài 12.
a)
2x x
2 2 6 6− + =
b)
2x x
3 3 5 5+ + =
c)
3

x x 1
8 1 2 2 1
+
+ = −
d)
x x 13
27 2 3 3 2
+
+ = −
Bài 13.
a)
x x
2 3 5+ =
b)
x x x
2 3 5+ =
c)
x
3 x 4 0+ − ≥
d)
( )
x
8 3x 1 4+ =
Bài 14.
a)
( )
x
x x x
9 5 4 2 20= + +
b)

(
)
2
3x x 1
2
3
1
log x 3x 2 2 2
5
− −
 
− + + + =
 ÷
 
Bài 15.
a)
( )
2x x x x
3 2 9 .3 9.2 0− + + =
b)
( )
x x
9 x 3 .3 2x 2 0+ − − + =
c)
( )
x 2 x 2
3.25 3x 10 .5 x 3
− −
+ − = −
d)

( ) ( )
2 x x
x 2 3 x 2 1 2 0+ − + − =
Bài 16.
a)
x x
3 5 6x 2+ = +
b)
x x
4 6 25x 2+ = +
c)
x x
3 .2x 3 2x 1= + +
Bài 17.
a)
( )
2
2
x 1 x x
2 2 x 1
− −
− = −
b)
2 2
x 4x 2 2x 8x 2 2
5 5 x 4x 2
+ + + +
− = + +
c)
2 2

x x 3 x 2 2 x 3 x x
2 9 x 6 4 3 5x
− − − −
+ + + = + +
Bài 18.
a)
x x 2
3 3 4 x
−
+ = −
b)
x 1 1 2x
3
2 2 3 2
+ −
+ =
c)
( )
2x 1 3 2x
2
3
8
2 2
log 4x 4x 4
+ −
+ =
− +
PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH LÔGARIT
Phương trình, bất phương trình mũ, lôgarit
Bài 1.

a)
( )
( )
2
2 2
log x 3 log 3x 5− = −
b)
( )
3 3 5
log x 6 log x 1 log 25+ + = +
c)
( )
( )
2
2 2
log x 3 log 6x 16 1 0− − − + ≤
d)
3 9 27
log x log x log x 11+ + ≥
Bài 2.
a)
( )
4 x
log x 2 .log 2 1+ =
b)
( ) ( )
2 2
2 2 2
log x 3x 2 log x 7x 12 3 log 3
+ + + + + = +

c)
( )
2
2
3 3
log x 2 log x 4x 4 9+ + + + ≥
d)
( )
5
1
2log x 1 log x log x
2
− = −
Bài 3.
a)
( )
( )
2
9 3 3
2 log x log x.log 2x 1 1= + −
b)
( ) ( )
2
3
3
log x 1 log 2x 1 2− + − =
c)
( ) ( )
3
1 8

2
2
log x 1 log 3 x log x 1 0+ − − − − =
d)
( ) ( ) ( )
8
4 2
2
1 1
log x 3 log x 1 log 4x
2 4
+ + − =
e)
( ) ( )
2 3
4 8
2
log x 1 2 log 4 x log 4 x+ + = − + +

Bài 4.
a)
( )
2
3 3
2log x 5log 9x 3 0− + =
b)
2 2
log x 3log x log x 4− < −
c)
2 2

2 1 4
2
2
log x 2log log x
x
− <
d)
3 x
5
log x log 3
2
+ =

Bài 5.
a)
( )
2 4 2
1
2 log x 1 .log x log 0
4
+ + =
b)
( ) ( )
x 1 x
2 2
log 4 4 .log 4 1 3
+
+ + =
c)
( ) ( )

x x 1
3 3
log 3 1 .log 3 3 6
+
− − =
d)
( )
3 3
3 log x log 3x 1 0− − =
Bài 6.
a)
3 3
2 1
1
1 log x 5 log x
+ =
+ −
b)
2
2x
x
log 64 log 16 3+ <
c)
2 2
4 2
3
4log x log x 2 0
2
− + ≥
d)

( )
3 9x
3
4
2 log x .log 3 1
1 log x
− − =
−
Bài 7.
a)
( )
2
log x 2 3 x− = −
b)
( )
2 3
log x log x 1 3+ − ≥
c)
( )
1 x
2
2 log 1 x
−
< +
d)
( )
2
2 2
log x x 1 log x 2x 6 0+ − + − =
Bài 8.

a)
( )
5 4
log x 1 log x+ =
b)
( )
3
2 7
log 1 x log x+ =
c)
( )
3
3 2
3log 1 x x 2log x+ + =
Bài 9.
Phương trình, bất phương trình mũ, lôgarit
a)
2
2
3
2
x x 3
log x 3x 2
2x 4x 5
+ +
= + +
+ +
b)
x
x

2
2 1
log 1 x 2
x
−
= + −
c)
( ) ( ) ( )
3 5 7
log 2x 1 log 4x 1 log 6x 1 3x+ + + + + =
Bài 10.
a)
( )
2 2
2 2
log 2x 4x 2 log x 1 4x 2x+ + − = + −
b)
( )
3
2
log x 1
2 2
2 2
3x 2 log x 1 log x
+
− = + −
Bài 11.
a)
( ) ( )
x 2x 1 x

1 1
2 2
log 4 4 log 2 3.2
+
+ ≥ −
b)
2
0,7 6
x x
log log 0
x 4
 
+
<
 ÷
+
 
c)
2
1
2
x 3x 2
log 0
x
− +
≥
d)
2
1
2

2x
log 4 5
4 x
 
− ≤
 ÷
−
 
Phương trình, bất phương trình mũ, lôgarit