Question

resolva as equações exponenciais:
a) $4 * 2^{2x} = 128$
b) $3^{5x-25} = 1$
c) $9^{x} = 27^{x-2}$
d) $7^{2x} = \frac{1}{49}$
e) $4^{x} = \sqrt[5]{64}$
f) $5^{2x-5}=125$
g) $2^{x} = 16$

Answer 1

a) 2^2 * 2^2x = 2^7
2 + 2x = 7
2x = 5
x = 5/2

b) 3^5x - 25 = 3^0
5x - 25 = 0
5x = 25
x = 25/5
x = 5

c) 3^2x = 3^3(x-2)
2x = 3x - 6
-x = -6 *(-1)
x = 6

d) 7^2x = 7^-2
2x = -2
x = -2/2
x = -1

e) 4^x = 64^1/5
2^2x = 2^6(1/5)
2x = 6/5
x =6/5 / 2
x = 6/5 * 1/2
x = 6/10
x = 3/5

f) 5^2x-5 = 5^3
2x - 5 = 3
2x = 8
x = 8/2
x = 4

g) 2^x = 2^4
x = 4