Answer
$x=3$
Work Step by Step
Note that $32=2^5$.
Write $32$ as $2^5$ to obtain:
$2^{2x-1}=2^5$
RECALL:
If $a^x = a^y$, then $x=y$.
Use the rule above to obtain:
$2^{2x-1}=2^5
\\2x-1=5
\\2x=5+1
\\2x=6
\\x=\frac{6}{2}
\\x=3$