how do you solve 2(2^2x)-5(2^x)+2=0 for x

Answer 1

Let 2^x = y
then your equation becomes
2y^2 - 5y + 2 = 0
(2y-1)(y-2) = 0
y = 1/2 or y = 2

then 2^x = 1/2 --- x = -1
or
2^x = 2 --- x = 1