#### Answer

$x=3$

#### Work Step by Step

We are given the exponential equation $2^{2x-1}=32$.
We can express each side using a common base and then solve for $x$.
$2^{2x-1}=2^{5}=32$
Take the natural log of both sides.
$ln(2^{2x-1})=ln(2^{5})$
$(2x-1)ln(2)=5ln(2)$
Divide both sides by $ln(2)$.
$2x-1=5$
Add 1 to both sides.
$2x=6$
Divide both sides by 2.
$x=3$