2^(2x-1) = 8^x

Let us simplify 8^x :

8= 2*2*2= 2^3

==> 2^(2x-1) = (2^3)^X)

==> 2^(2x-1) = 2^3x

The bases are equal, then the powers are equal:

==> 2x-1= 3x

==> x=-1

To check:

2^(2x-1)= 8^x

2^(2(-1)-1) = 8^-1

2^(-3)=8^-3

1/ 2^3 = 1/8

1/8 = 1/8