D ng 1: Cùng mũ , cùng c s .ạ ơ ố
a)
3 2cos 1 cos
4 7.4 2 0
x x
+ +
− − =
b)
2 2
1 3
16 64 4 3 0
x x− −
− ⋅ + =
c)
9 9 3
log log log 27
4 6 2 2 0
x x
− ⋅ + =
d)
2 2
2 2 1
9 7 3 2
x x x x x x
− − − − −
− ⋅ =
e)
2 2
sin cos
9 9 10
x x
+ =
f)
1 3
3
64 2 12 0
x x
+
− + =
g)
2
cos2 cos
4 4 3
x x
+ =
h)
2 2
4 6.2 8 0
x x
− + =
i)
k)
x x
x x
−
−
− ≤
2
22
21
9 2 3
3
D ng 2: Cùng mũ , khác c s .ạ ơ ố
a)
2 2 2
15.25 34.15 15.9 0
x x x
− + =
b)
1 1 1
6.9 13.6 6.4 0
x x x
− + =
c) 125x + 50x = 23x + 1
d)3 x + 1 – 22x + 1 – 12x/2 < 0
e) 4.3x – 9.2x = 5.6x/2
f)
3 3 3
25 9 15 0
x x x
− + =
D ng 3: Cùng c s , khác mũ.ạ ơ ố
a) 9. > 0
b) + = 0
c)
1
4 4 3.2
x x x x+ +
− =
D ng 4: Nhóm phân tích th a s .ạ ừ ố
a)12.3x + 3.15x – 5x +1 = 20
b)8.3x + 3.2x = 24 + 6x.
D ng 5: Tích c s b ng 1.ạ ơ ố ằ
a)
( ) ( )
2 3 2 3 14
x x
− + + =
b)
()()
4 15 4 15 8
x x
− + + =
c)
()()
cos cos
5
7 4 3 7 4 3 2
x x
+ + − =
d)
( ) ( )
7 3 5 7 3 5 14.2
x x
x
+ + − =
e)
()()
2 3 2 3 2
x x
x
+ + − =
D ng 1: Đ a v cùng c s .ạ ư ề ơ ố
a)
2
2 2
log ( 1) 6log 1 2 0x x+ − + + =
b)
2 2
2 1 1
log (2 1) log (2 1) 4
x x
x x x
− +
+ − + − =
c)
2
5 5
log 2log 15 0x x− − >
d)
3 3
log ( 1) log (11 ) 3x x+ + − <
e)
22
log 2 2 log 4 log 8 0
x x x
+ + =
f)
2 8
2
5
log log log 3
x x x+ + =
g)
2
2 1 2
2
1log ( 1) log ( 4) log (3 )
2
x x x
− + + = −
h)
3 1
3
2log (4 3) log (2 3) 2x x
− + + ≤
i)
( )
3 9
3
4
2 log log 3 1
1 log
x
x
x
− − =
−
D ng 2:ạmũ hóa.
a)
( )
7 3
log log 2x x= +
b)
( )
4
12 3
1
log log
2
x x x+ =
c)
( )
2 3
log 1 logx x+ =
d)
( )
5 7
log log 2x x= +
e)
( ) ( )
2 1
1 1
2 2
log 4 4 log 2 3.2
x x x+
+ ≥ −
f)
2 2
1
log (4 15 2 27) 2 log 0
4 2 3
x x
x
+ ⋅ + + =
⋅ −
g)
3
log (log (9 72)) 1
x
x
− ≤
h)
2
5 5 5
log (4 144) 4 log 2 1 log (2 1)
x x−
+ − < + +
D ng 3: ạcùng c s , cùng n .ơ ố ẩ
a)
( )
3 9
3
4
2 log log 3 1
1 log
x
x
x
− − =
−
b)
( )
2
4 2
log 8 log log 2 0
xx x+ ≥
c)
2
1 4
2
3 log log 2 0x x+ − >
d)
( ) ( )
x x 1
3 3
log 3 1 log 3 3 6
+
− − =
e)
2 2
log 10log 6 9x x+ + =
f)
1
5 25
log (5 1) log (5 5) 1
x x+
− ⋅ − =
g)
2
3 3
log 5log 6 0x x− + =
h)
2
6 6
log log
6 12
x x
x+ ≤
i)Gpt:
2 2
3 3
log log 1 2 1 0x x m+ + − − =
a) Gi i ph ng trình khi m = 2.ả ươ
b) Tìm m đ ph ng trình có ít nh t m t nghi m thu c đo n ể ươ ấ ộ ệ ộ ạ
3
1;3
D ng 4: ạC s là bi n.ơ ố ế
Bài 1. >2
Bài 2. >1
Các d ng toán thiạ
Bài 1.
2 4
0,5 2 16
log 4.log 2.(4 log )x x x+ ≤ −
Bài 2.
()
2
2
4
log log 2 0x x x
π
+ − <
Bài 3.
( )
5
log 5 4 1
xx− = −
Bài 4.
3 1
3
2log (4 3) log (2 3) 2x x− + + ≤