Bài 4 :
a) 2^x = 4^3
<=> 2^x = 2^6
<=> x = 6
b) 2^x = 4^6
<=> 2^x = 2^12
<=> x = 12
c) 3^x = 9^10
<=> 3^x = 3^20
<=> x = 20
d) 2^x = 8^3
<=> 2^x = 2^9
<=> x = 9
e) 2^x = 8^9
<=> 2^x = 2^27
<=> x = 27
f) (1/5)^x = (1/125)^3
<=> (1/5)^x = (1/5)^9
<=> x = 9

4) (5/6)^(2x - 1) = 5/6^6
<=> 2x - 1 =6
<=> 2x = 7
<=> x = 7/2
vậy x = 7/2
6) (-1/10)^x = 1/100
<=> (-1/10)^x = (-1/10)^2
<=> x = 2
vậy x = 2
7) (-1/10)^x = 0,01
<=> (-1/10)^x = 1/100
<=> (-1/10)^x = (-1/10)^2
<=> x = 2
vậy x = 2

8) (-3/2)^x = 9/4
<=> (-3/2)^x = (-3/2)^2
<=> x = 2
vậy x = 2
9) (-3/5)^x = 9/25
<=> (-3/5)^x = (-3/5)^2
<=> x = 2
10) (-2/3)^x = -8/27
<=> (-2/3)^x = (-2/3)^3
<=> x = 3

bài 4
a) 2^x = 4^3
<=> 2^x = (2^2)^3
<=> 2^x = 2^6
<=> x = 6
vậy x = 6
b) 2^x = 4^6
<=> 2^x = (2^2)^6
<=> 2^x = 2^12
<=> x = 12
c) 3^x = 9^10
<=> 3^x = (3^2)^10
<=> 3^x = 3^20
<=> x = 20
vậy x = 20

bài 4
4) 2^x = 8^3
<=> 2^x = (2^3)^3
<=> 2^x = 2^9
<=> x = 9
vậy x = 9
5) 2^x = 8^5
<=> 2^x = (2^3)^5
<=> 2^x = 2^15
<=> x = 15
vậy x = 15
6) (1/5)^x = (1/125)^3
<=> (1/5)^x = [(1/5)^3]^3
<=> (1/5)^x = (1/5)^9
<=> x = 9
vậy x = 9

bài 7
7) (1/7)^x = (1/343)^3
<=> (1/7)^x = [(1/7)^3]^3
<=> (1/7)^x = (1/7)^9
<=> x = 9
vậy x = 9
8) (2/3)^x = (4/9)^4
<=> (2/3)^x = [(2/3)^2]^4
<=> (2/3)^x= (2/3)^8
<=> x = 8
vậy x = 8
9) (3/5)^x = (9/25)^3
<=> (3/5)^x = [(3/5)^2]^3
<=> (3/5)^x = (2/5)^6
<=> x =6
vậy x = 6

bài 4
10) (6/7)^x = (216/343)^111
<=> (6/7)^x = [(6/7)^3]^111
<=> (6/7)^x=(6/7)^333
<=> x = 333
vậy x = 333
11) 3^(2x + 2) = 9^10
<=> 3^(2x + 2) = (3^2)^10
<=> 3^(2x + 2) = 3^20
<=> 2x + 2 = 20
<=> 2x=18
<=> x= 9
vậy x = 9
12) 2^(3 - 2x) = 8^3
<=> 2^(3 - 2x) = (2^3)^3
<=> 2^(3 - 2x)=2^9
<=> 3 - 2x = 9
<=> 2x = -6
<=> x = -3
vậy x = -3

câu 4
13) 2^(5x + 2) = 8^9
<=> 2^(5x +2) = (2^3)^9
<=> 2^(5x + 2)= 2^27
<=> 5x + 2 = 27
<=> 5x = 25
<=> x = 5
vậy x = 5
14) 2^(6 + 5x) = 16^9
<=> 2^(6 + 5x) = (2^4)^9
<=> 2^(6 + 5x) = 2^36
<=> 6 + 5x = 36
<=> 5x = 30
<=> x = 6
vậy x = 6
15) 2^(3x + 1) = 32^2
<=> 2^(3x + 1) = (2^5)^2
<=> 2^(3x + 1) = 2^10
<=> 3x + 1 = 10
<=> 3x = 9
<=> x = 3
vậy x = 3

câu 4
17) 3^(3 - 2x) = 27^13
<=> 3^(3 - 2x) = (3^3)^13
<=> 3^(3 - 2x) = 3^39
<=> 3 - 2x = 39
<=> 2x = -36
<=> x = -18
vậy x = -18
18) 3^(6 - 3x) = 81^3
<=> 3^(6 - 3x) = (3^4)^3
<=> 3^(6 - 3x) = 3^12
<=> 6 - 3x = 12
<=> 3x = -6
<=> x = -2
vậy x = -2

cau 4
19) 4^(-1-5x)= 16^12
<=> 4^(-1-5x) = (4^2)^12
<=> 4^(-1-5x) = 4^24
<=> -1 - 5x = 24
<=> 5x = -25
<=> x = -5
vậy x =-5
20) 5^(2x + 1) = 125^(x + 25)
<=> 5^(2x + 1) = 5^(3x + 75)
<=> 2x + 1 = 3x + 75
<=> x = -74
vậy x = -74
câu 5
1) 4^x = 8^4
<=> 2^2x = 2^12
<=> 2x = 12
<=> x = 6
vậy x = 6
2) 4^x = 32^24
<=> 2^2x = 2^(5.24)
<=> 2^2x = 2^120
<=> 2x = 120
<=> x = 60
vậy x = 60

câu 5
3) 8^x = 16^12
<=> (2^3)^x = (2^4)^12
<=> 2^3x = 2^48
<=> 3x = 48
<=> x = 16
vậy x = 16
4) 4^x = 8^12
<=> (2^2)^x = (2^3)^12
<=> 2^2x = 2^36
<=> 2x = 36
<=> x = 18
vậy x = 18
5) 4^x = 32^40
<=> (2^2)^x = (2^5)^40
<=> 2^2x = 2^200
<=> 2x =200
<=> x = 100
vậy x = 100
6) 8^x = 32^9
<=> (2^2)^x=(2^5)^9
<=> 2^2x = 2^45
<=> 2x = 45
<=> x = 45/2
vậy x = 45/2

bài 5
7) 8^x = 16^99
<=> (2^3)^x = (2^4)^99
<=> 2^3x = 2^396
<=> 3x = 396
<=> x = 132
vậy x = 132
8) 8^x = 32^33
<=> (2^3)^x = (2^5)^33
<=> 2^3x = 2^165
<=> 3x = 165
<=> x = 55
vậy x = 55
9) 8^x = 32^66
<=> (2^3)^x = (2^5)^66
<=> 2^3x = 2^330
<=> 3x = 330
<=> x = 110
vậy x = 110

bài 5
10) 16^x =32^8
<=> (2^4)^x = (2^5)^8
<=> 2^4x = 2^40
<=> 4x = 40
<=> x =10
vậy x =10
11) 32^x = 16^10
<=> (2^5)^x = (2^4)^10
<=> 2^5x = 2^40
<=> 5x = 40
<=> x = 8
vậy x = 8
12) 16^x = 64^10
<=> (4^2)^x = (4^3)^10
<=> 4^2x = 4^30
<=> 2x = 30
<=> x = 15
vậy x = 15
13) 10000^x = 1000^24
<=> (10^4)^x = (10^3)^24
<=> 10^4x = 10^72
<=> 4x = 72
<=> x = 18
vậy x = 18