Question

Resolva, em R, as seguintes equações exponenciais :
8^x =16

27^x =9

4^x=32

25^x =625

9^x =1/27

4^x =1/2

(1/25)^x =125

(1/4)^x =1/8

Answer 1

A) 8^x = 16

8^x = 16
(2³)^x = 2^4
2^3x = 2^4
3x = 4
x = 4/3

B) 27^x = 9

27^x = 9
(3³)^x = 3^2
3^3x = 3^2
3x = 2
x = 2/3

C) 4^x = 32

4^x = 32
(2²)^x = 2^5
2^2x = 2^5
2x = 5
x = 5/2

D) 25^x = 625

25^x = 625
(5²)^x = 5^4
5^2x = 5^4
2x = 4
x = 4/2
x = 2

E) 9^x = 1/27

9^x = 1/27
(3²)^x = 1/(3³)
3^2x = 3^(- 3)
2x = - 3
x = - 3/2

F) 4^x = 1/2

4^x = 1/2
(2²)^x = 2^(- 1)
2^2x = 2^(- 1)
2x = - 1
x = - 1/2

G) (1/25)^x = 125

(1/25)^x = 125
(1/5²)^x = 5^3
(5^(- 2))^x = 5^3
5^(- 2x) = 5^3
- 2x = 3 . (- 1)
2x = - 3
x = - 3/2

H) (1/4)^x = 1/8

(1/4)^x = 1/8
(1/2²)^x = 1/2³
(2^(- 2))^x = 2^(- 3)
2^(- 2x) = 2^(- 3)
- 2x = - 3 . (- 1)
2x = 3
x = 3/2