Find all real solutions x to

Question

(4^x)-(2^x)=56. Please explain in steps! Thank you.

Answer 1

(4^x)-(2^x)=56
(2^2)^x - 2^x - 56 = 0
(2^x)^2 - 2^x - 56 = 0
let 2^x = t , we get
t^2 - t - 56 = 0
(t-8)(t+7) = 0
t = 8 or t = -7

if t = -7
2^x = -7 , no such x exists
or
if t = 8
2^x = 8 -----> x = 3