Phương trình mũ và lôgarít phần - thầy toán

Phương trình mũ và lôgarít
Giải các phương trình sau
1
2 3 2 3 5 5
3 .5 3 .5
x x x x
+ +
=
2
255
4
2
=
+−
xx
3
− + −
− =
2
x x 8 1 3x
2 4 0
4
2
3 2
4 16 0
x x
− +
− =
5
( ) ( )
1

1
1
2525
+
−
−
−=+
x
x
x
6
x
x
34
2
2
2
1
2
−
−
=






7
2 3

3 3
1
9 27 81
3
x
x x x
−
+
 
=
 ÷
 
8
−
   
=
 ÷  ÷
   
x x 1
8 9
27 4
9
3
3
1
13
=







−
x
10
2 1 2 1
2 2
2
(2 3) (2 3)
2 3
x x x x
− + − +
+ + − =
−
11
7 1
3 9 27
.
2 4 8
x x+ +
   
=
 ÷  ÷
   
12
1
5
93
2

+
−
=
x
x
13
9 5.3 7 0
x x
+ + =
14
2 2
3 3 30
x x
+ −
+ =
15
4 2 6 0
x x
+ − =
16
2 1
3 9 4
x x
+ +
+ =
17
2( 1)
3 82.3 9 0
x x
+

− + =
18
25 23.5 5 0
x x
− − =
19
8 18 2.27
x x x
+ =
20
1 3
2 2
9 36.3 3 0
x x
− −
+ + =
21
4 2 5 3
2
3 9
x x x
− − −
=
22
3 3 2 2
3 .7 3 .7
x x x x
+ +
=
23

1 1
3 3 3 9477
x x x− +
+ + =
24
10
5
14
( 3) ( 3) 84 0
x x
−
+ − =
25
1 1 1
49 35 25
x x x
− =
26
(2 3) (2 3) 14
x x
− + + =
27
2
2
1
.
2
1
217
=













−+
xx
28
2
2
9 10 4
2 4
x
x
−
+
=
29
3 3
5 9.5 27(5 5 ) 64
x x x x
− −
+ + + =

30
3
(5 21) 7(5 21) 2
x x x
+
− + + =
31
2 4 2 2
3 45.6 9.2 0
x x x
+ +
+ − =
32
3
3 1
8 1
2 6(2 ) 1
2 2
x x
x x
−
− − − =
33
1
5 7
2
(1,5)
3
x
x

+
−
 
=
 ÷
 
34
( )
2
ln 1
1
25 . 1 0
5
x
x
e
−
 
 
− − =
 ÷
 ÷
 ÷
 
 
35
2 3
( 2 1) 2 1
x−
− = +

36
4 11 32 13
x x x x
+ + =
37
2 2 1
9.2 8 3
x x
+
=
38
1
4 4
8.3 9 9
x x x x
+ +
+ =
39
9 2( 2)3 2 5 0
x x
x x
+ − + − =
40
4x 8 2x 5
3 4.3 27 0
+ +
− + =
41
x x
(2 3) (2 3) 4 0

+ + − − =
42
x x
2.16 15.4 8 0
− − =
43
2x 6 x 7
2 2 17 0
+ +
+ − =
44
25 2(3 )5 2 7 0
x x
x x
− − + − =
45
2 1 1
3 4.3 27 0
x x
+ +
− + =
46
2
3 3 8 0
x x
− +
− + =
47
(
)

(
)
4 15 4 15 8
x x
− + + =
48
( ) ( )
2 3 2 3 4 0
x x
+ + − − =
49
2 3. 2 17 11
x x
− + =
50
x x
(7 4 3) 3(2 3) 2 0
+ − − + =
51
2 2
sin x os
81 81 30
c x
+ =
52
(1 2) 2.(1 2) 3
x x
+ + − =
53
x x x 3

(3 5) 16(3 5) 2
+
+ + − =
54
x
3 x 4 0+ − =
1
Phương trình mũ và lôgarít
55
1 1 1
x x x
2.4 6 9
+ =
56
2 3x 3
x x
8 2 12 0
+
− + =
57
x x x
3 4 5+ =
58
2 1 3
2 2 64 0
x x+ +
− − =
59
x x x
3.16 2.8 5.36

+ =
60
x x 1 x 2 x x 1 x 2
5 5 5 3 3 3
+ + + +
+ + = + +
61
1 2
2
2 2 ( 1)
x x x
x
− −
− = −
62
1 4 2
4 2 2 16
x x x
+ + +
+ = +
63
25 2(3 )5 2 7 0
x x
x x
− − + − =
64
3 5 6 2
x x
x
+ = +

65
( ) ( )
2 2
log log
2 2 2 2 1
x x
x x
+ + − = +
66
( ) ( ) ( )
3 2 3 2 5
x x x
− + + =
67
2 2
2x 4 2 2 1
2 4.2 2 0
x x x− − − +
− − =
68
2 2
2x 2 1
3 28.3 9 0
x x x+ + +
− + =
69
2 2
x 1 2
9 10.3 1 0
x x x+ − + −

− + =
70
( )
−
− =
3 x
x-1
4 0,5 62
71
2x+1 2 1
3 2 5.6 0
x x+
− − =
72
3x+1 2
2 7.2 7.2 2 0
x x
− + − =
73
− − =
x x x
36 2 .3 6 0.
74
− − =
4x 2 x 2x 2 x
4.5 29.2 .3 25.2 0
75
( ) ( )
+ +
   

− + =
 ÷  ÷
   
3 x 3 3 x 3
25 5
5. 7. 2 0
4 2
76
   
− + =
 ÷  ÷
   
2x 2 x
16 4
3. 7. 4 0
9 3
77
( )
+
+ + + =
x x x 1
3
3 3 2 3 log 81 0.
78
( )
− + − =
2
x x
2
2 2 2 log 4 0.

79
( ) ( )
− + + − =
2
2x 2x 2x
3 2 3 3 1 2 0
80
( )
− + + =
2
3x 3x
2
2 2 2 log 8 0
81
222
21212
15.34925
xxxxxx
−+−+−
=+
82
1 1 1
3.16 2.81 5.36
x x x+ + +
+ =
83
2 2 2
2 2 2
6.9 13.6 6.4 0
x x x x x x− − −

− + =
84
2 1
25 10 2
x x x
+
+ =
85
02.96.453
2242
=−+
++
xxx
86
− − −
+ =3.16 2.81 5.36
x x x
87
2 2 2
6.9 13.6 6.4 0
x x x
− + =
88
+ −
− =
3x x 3x 1 x 1
2 .3 2 .3 192
89
+ +
− = −

x+4 x 3 x x 2
3 5 3 5
90
111
9)32(2
−−−
=+
xxxx
91
−
   
=
 ÷  ÷
   
x 3 x
x
1 1
5
5 125
92
2
2
2
x 2
1
9 2. 3
3
x x
x
−

−
 
− =
 ÷
 
93
+ =
− +
1 2
1
4 2 2 2
x x
94
= −
− +
2 2
1 3
1
5 5 3 5
x x
95
+ =
+
x x
1 2
1
5-25 1 25
96
−
+ =

-x 1 x
3 2 4
3
1+3 3
Giải các phương trình sau
97
3 9
3log log 5x x
− =
98
2 2
log ( 3) log ( 1) 3x x
− + − =
99
3 1
3
6
log (1 ) log 0
2
x
x
− + =
−
100
2
2
log 64 log 16 3
x
x
+ =

101
7 1
7
3 2
log log 0
21 3 6
x
x
+
+ =
−
102
2
2 1 1 2
2 4
log ( 3) log 5 2log ( 1) log ( 1)x x x
+ + = − − +
103
2 1
8
log ( 2) 2 6log 3 5x x
− − = −
104
2
2 2
log ( 1)log 2 6 0x x x x
+ − + − =
2
Phương trình mũ và lôgarít
105

5 25 0,2
log x log x log 3
+ =
106
2 4
log 4 log 5 0x x
− − =
107
3 9 27
5
log log 3 log
3
x x x
+ + =
108
2
5
log log 2
2
x
x
+ =
109
2 2
3 7 2 3
log (4 12 9) log (6 23 21) 4
x x
x x x x
+ +
+ + + + + =

110
( ) ( )
5 5 5
log x log x 6 log x 2
= + − +
111
3 2
9
9
9
2
5log log 8log 2
x
x
x
x x x
+ + =
112
2
x 3
lg(x 2x 3) lg 0
x 1
+
+ − + =
−
113
1 2
1
4 lg x 2 lg x
+ =

− +
114
1 3
5
1
log log 2 0
3
x
 
− =
 
 
115
( )
2
x
log 2x 5x 4 2− + =
116
2 2
log x 10 log x 6 0
+ + =
117
0,04 0,2
log x 1 log x 3 1+ + + =
118
( ) ( )
x x
2 2
log 4.3 6 log 9 6 1
− − − =

119
− + + = +
1
lg(5x 4) lg x 1 2 lg 0,18
2
120
( ) ( )
x 1 x
2 2 1
2
1
log 4 4 .log 4 1 log
8
+
+ + =
121
x
3 9
1
log log x 9 2x
2
 
+ + =
 ÷
 
122
( )
x x
lg 6.5 25.20 x lg25+ = +
123

( )
( ) ( )
x 1 x
2 lg2 1 lg 5 1 lg 5 5
−
− + + = +
124
( )
x
x lg 4 5 x lg2 lg3+ − = +
125
2
56
32 1
log 16 3
log 2
x
x
x x
 
− = −
 ÷
 
126
2
32
1 75 11
3 log
4
log

2
x
x
x
x
 
+ = −
 ÷
 
127
2 2
3 3
log ( 1) log 2x x x x x
+ + − = −
128
1
5 25
log (5 1).log (5 5) 1
x x
+
− − =
129
2
2
3
2
3
log 3 2
2 4 5
x x

x x
x x
 
+ +
= + +
 ÷
+ +
 
130
( ) ( )
2 2
2
log log
2 2 2 2 1
x x
x x
+ + − = +
131
7 3
log log ( 2)x x
= +
132
2 2
3 3
log log 1 5 0x x
+ + − =
133
2
log ( 1) 1x x
 

− =
 
134
2 2
log log ( 1) 1x x
+ − =
135
2 1/8
log ( 2) 6.log 3 5 2x x
− − − =
136
2 2
log ( 3) log ( 1) 3x x
− + − =
137
4 4 4
log ( 3) log ( 1) 2 log 8x x
+ − − = −
138
lg( 2) lg( 3) 1 lg 5x x
− + − = −
139
lg 5 4 lg 1 2 lg 0,18x x− + + = +
140
8 8
2
2 log ( 2) log ( 3)
3
x x
− − − =

141
2
3 3
log ( 6) log ( 2) 1x x
− = − +
142
2 2 5
log ( 3) log ( 1) 1/ log 2x x
+ + − =
143
4 4
log log (10 ) 2x x
+ − =
144
5 1/ 5
log ( 1) log ( 2) 0x x− − + =
145
2 2 2
log ( 1) log ( 3) log 10 1x x− + + = −
146
9 3
log ( 8) log ( 26) 2 0x x
+ − + + =
147
3 1/3
3
log log log 6x x x+ + =
148
4 1/16 8
log log log 5x x x

+ + =
149
2 2
1 lg( 2 1) lg( 1) 2 lg(1 )x x x x
+ − + − + = −
150
1/2 1/2
1/ 2
log ( 1) log ( 1) 1 log (7 )x x x
− + + = + −
151
2 2
2 lg(4 4 1) lg( 19) 2 lg(1 2 )x x x x
+ − + − + = −
152
2 4 8
log log log 11x x x
+ + =
153
2 2 3 3
log log log logx x
=
154
2 3 3 2
log log log logx x
=
155
2 3 3 2 3 3
log log log log log logx x x
+ =

156
2 3 4 4 3 2
log log log log log logx x
=
157
2
log (9 2 ) 3
x
x
− = −
158
3
log (3 8) 2
x
x
− = −
3
Phương trình mũ và lôgarít
159
7
log (6 7 ) 1
x
x
−
+ = +
160
1
3
log (4.3 1) 2 1
x

x
−
− = −
161
5
log (3 )
2
log (9 2 ) 5
x
x
−
− =
162
( ) ( )
155log.15log
1
255
=−−
+
xx
163
2
log (12 2 ) 5
x
x
− = −
164
1
2
log (5 25 ) 2

x x
+
− =
165
2
log (3.2 1) 2 1 0
x
x
− − − =
166
1
1
6
log (5 25 ) 2
x x
+
− = −
167
5
log (26 3 ) 2
x
− =
168
( )
( )
2 4
1
log 2 1 .log 2 2 1
x x+
− − =

169
1
4
log (3.2 5)
x
x
+
− =
170
( ) ( )
2
2 2
3
log 4.3 6 log 9 6 1
2
x x
− − − =
171
1
1
5
log (6 36 ) 2
x x
+
− = −
172
( )
15log.5log
22
5

=
x
x
173
2 2
3 3
log log 1 5 0x x
+ + − =
174
5
1
2 log 2 log
5
x
x
− =
175
2
2 1/2
2
log 3log log 2x x x
+ + =
176
2 2
3 log log 4 0x x− =
177
4
7
log 2 log 0
6

x
x
− + =
178
3 3
3 log log 3 1 0x x− − =
179
2
2 1/2
2
log 3log log 0x x x
+ + =
180
3
3
2 2
log log 4 / 3x x+ =
181
5
1
log log 2
5
x
x
− =
182
3
3
2 2
log log 2 / 3x x− = −

183
2
2
log 16 log 64 3
x
x
+ =
184
2
2 4
1
log 2 log 0x
x
+ =
185
7
1
log log 2
7
x
x
− =
186
2
2
1 2
2
log 4 log 8
8
x

x
+ =
187
2
2 1/4
log (2 ) 8log (2 ) 5x x
− − − =
188
2
5 25
log 4 log 5 5 0x x
+ − =
189
2
9
log 5 log 5 log 5
4
x x x
x
+ = +
190
2
9
log 3 log 1
x
x+ =
191
1 2
1
4 lg 2 lgx x

+ =
− +
192
2 3
2 16 4
log 14 log 40 log 0
x x x
x x x
− + =
193
( )
2
9 3 3
2 log log .log ( 2 1 1)x x x
= + −
194
2 2 4 2 4 2
log ( 1) log ( 1) log ( 1) log ( 1)
2 2 2 2
x x x x x x x x
+ + + − + = + + + − +
195
2 2
2 2 2
log ( 3 2) log ( 7 12) 3 log 3x x x x
+ + + + + = +
196
2 2 2
4 5 20
log ( 1).log ( 1) log ( 1)x x x x x x

− − + − = − −
4