Answer
$x=\dfrac{8}{5}$
Work Step by Step
$32^{2x-3}=2$
Rewrite $32$ as $2^{5}$:
$(2^{5})^{2x-3}=2$
Multiply the exponents:
$2^{10x-15}=2$
If $2^{10x-15}=2$, then $10x-15=1$:
$10x-15=1$
Solve for $x$:
$10x=1+15$
$10x=16$
$x=\dfrac{16}{10}$
$x=\dfrac{8}{5}$