32(2)^2x-12(2)^x+1=0

Question

I've spent too much time trying to figure this out. Please help.

Answer 1

32(2)^2x-12(2)^x+1=0

Recall that 2^2x = (2^x)^2, so you have

32(2^x)^2 - 12(2^x) + 1 = 0

Now, just to make things easier to read, let u = 2^x and you have

32u^2 - 12u + 1 = 0
(8u-1)(4u-1) = 0
u = 1/8 or 1/4

So, that means we have

2^x = 1/8 ------> x = -3
2^x = 1/4 ------> x = -2