Question

Please explain how to get to step 2. Question attached.

Answer 1

I think there's an error in step 1.
Basically, the equation was multiplied by 2,
2^2x-3*2^x+2=0

Answer 2

Now, if you take 2^x=t
t^2-3t+2=0
(t-1)(t-2)=0

Answer 3

that is, 2^x=1, i.e. x=0
OR 2^x=2, i.e. x=1

Answer 4

to change the exponent from 2x-1 to 2x, how did that happen?

Answer 5

You multiply the eqn by 2.

What happened was 2^1*2^x-1=2^(x-1+1)=2^x