Question

2^2x-1 - 3 times 2^x-1 + 1 = 0

Answer 1

if either term is 0, the whole thing is zero, so this is two problems:
a) 2^(2x-1) - 3 = 0
or
b) 2^(x-1) + 1 = 0
NOTE - You did not give me parentheses, so I am guessing what you mean.
problem a
2^(2x-1) = 3
(2x-1) log 2 = log 3
(2x-1) = .477/.301 = 1.58
2x = 2.58
x = 1.29
or
problem b
2^(x-1) = -1
there is no such thing as log -1. I am stuck, no solution
the question is: Two to what power = -1
There is no such power.
therefore the only solution is problem a