Question

Помогите пожалуйста 8^х-4^х=2^х

Answer 1

8^х-4^х=2^х
(2^3)^x - (2^2)^x = 2^x
(2^x)^3 - (2^x)^2 = 2^x
t = 2^x, t > 0
t^2 - t - 1 = 0
t^2 - t + 1/4 - 1/4 - 1 = 0
(t - 1/2)^2 = 5/4
t - 1/2 = +- sqrt(5)/2
t = (1 +- sqrt(5))/2 = {t > 0} = (1 + sqrt(5) ) / 2 = 2^x
x = log2(1/2 + sqrt(5)/2) = log2(1 + sqrt(5)) - 1