Phương trình,bất phương trình mũ,lôgrit

Ph¬ng tr×nh, bÊt ph¬ng tr×nh mò vµ l«garÝt.
Bµi 1: Gi¶i ph¬ng tr×nh:
a.
2
x x 8 1 3x
2 4
− + −
=
b.
2
5
x 6x
2
2 16 2
− −
=
c.
x x 1 x 2 x x 1 x 2
2 2 2 3 3 3
− − − −
+ + = − +
d.
x x 1 x 2
2 .3 .5 12
− −
=
e.
2
2 x 1
(x x 1) 1
−

− + =
f.
2 x 2
( x x ) 1
−
− =
g.
2
2 4 x
(x 2x 2) 1
−
− + =
h,
2
2 2
3 5 2 4
( 3) ( 6 9)
x x x x
x x x
− + + −
− = − +
Bµi 2:Gi¶i ph¬ng tr×nh:
a.
4x 8 2x 5
3 4.3 27 0
+ +
− + =
b.
2x 6 x 7
2 2 17 0

+ +
+ − =
c.
x x
(2 3) (2 3) 4 0+ + − − =
d.
x x
2.16 15.4 8 0− − =
e.
x x x 3
(3 5) 16(3 5) 2
+
+ + − =
f.
x x
(7 4 3) 3(2 3) 2 0+ − − + =
g.
x x x
3.16 2.8 5.36+ =
h.
1 1 1
x x x
2.4 6 9+ =
i.
2 3x 3
x x
8 2 12 0
+
− + =
j.

x x 1 x 2 x x 1 x 2
5 5 5 3 3 3
+ + + +
+ + = + +
k.
x 3
(x 1) 1
−
+ =
t,
( ) ( )
10245245
=−++
xx
m,
( ) ( )
3
2531653
+
=−++
x
xx
n,
( ) ( )
02323347
=+−−+
xx
Bµi 3:Gi¶i c¸c hÖ ph¬ng tr×nh:
a.
x y

3x 2y 3
4 128
5 1
+
− −

=


=


b.
2
x y
(x y) 1
5 125
4 1
+
− −

=


=


b.
2x y
x y

3 2 77
3 2 7

− =


− =


d.
x y
2 2 12
x y 5

+ =

+ =

Bµi 4: Gi¶i c¸c bÊt ph¬ng tr×nh sau:
a.
6
x
x 2
9 3
+
<
b.
1
1
2x 1

3x 1
2 2
−
+
≥
c.
2
x x
1 5 25
−
< <
d.
2 x
(x x 1) 1− + <
Bµi 5: Gi¶i c¸c bÊt ph¬ng tr×nh sau:
a.
x x
3 9.3 10 0
−
+ − <
b.
x x x
5.4 2.25 7.10 0+ − ≤
c.
x 1 x
1 1
3 1 1 3
+
≥
− −

d.
2 x x 1 x
5 5 5 5
+
+ < +
e.
x x x
25.2 10 5 25− + >
f.
x x 2 x
9 3 3 9
+
− > −
Bµi 6: Gi¶i c¸c ph¬ng tr×nh:
a.
( ) ( )
5 5 5
log x log x 6 log x 2= + − +
b.
5 25 0,2
log x log x log 3+ =
c.
( )
2
x
log 2x 5x 4 2− + =
d.
2
x 3
lg(x 2x 3) lg 0

x 1
+
+ − + =
−
Bµi 7: Gi¶i c¸c ph¬ng tr×nh sau:
a.
1 2
1
4 lgx 2 lg x
+ =
− +
b.
2 2
log x 10 log x 6 0+ + =
c.
0,04 0,2
log x 1 log x 3 1+ + + =
d.
x 16 2
3log 16 4log x 2 log x− =
e.
2
2x
x
log 16 log 64 3+ =
f.
3
lg(lgx) lg(lgx 2) 0+ − =
Bµi 8: Gi¶i c¸c hÖ ph¬ng tr×nh:
a.

2 2
lgx lgy 1
x y 29
+ =


+ =

b.
3 3 3
log x log y 1 log 2
x y 5
+ = +


+ =

Bµi 9: Gi¶i bÊt ph¬ng tr×nh:
a.
( )
2
8
log x 4x 3 1− + ≤
b.
3 3
log x log x 3 0− − <
c.
( )
2
1 4

3
log log x 5 0
 
− >
 
d.
( )
( )
2
1 5
5
log x 6x 8 2log x 4 0− + + − <
e.
1 x
3
5
log x log 3
2
+ ≥
f.
( )
x
x 9
log log 3 9 1
 
− <
 
h.
1
3

4x 6
log 0
x
+
≥
i.
( ) ( )
2 2
log x 3 1 log x 1+ ≥ + −
j.
8 1
8
2
2log (x 2) log (x 3)
3
− + − >
k.
3 1
2
log log x 0
 
≥
 ÷
 ÷
 
l.
5 x
log 3x 4.log 5 1+ >
m.
2

3
2
x 4x 3
log 0
x x 5
− +
≥
+ −
n.
1 3
2
log x log x 1+ >
o.
( )
2
2x
log x 5x 6 1− + <
p.
( )
2
3x x
log 3 x 1
−
− >
r.
x 6 2
3
x 1
log log 0
x 2

+
−
 
>
 ÷
+
 
s.
2
2 2
log x log x 0+ ≤
x,
2
65
3
1
3
1
2
+
−+
>
x
xx
Bµi 10: Gi¶i hÖ bÊt ph¬ng tr×nh:
a.
2
2
x 4
0

x 16x 64
lg x 7 lg(x 5) 2 lg2

+
>

− +


+ > − −

b.
( )
( ) ( )
( )
x 1 x
x
x 1 lg2 lg 2 1 lg 7.2 12
log x 2 2
+

− + + < +


+ >

