Answer
$x=\frac{8}{5}$
Work Step by Step
We are given that $32^{2x-3}=2$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{5})^{2x-3}=2^{10x-15}=2^{1}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $10x-15=1$.
Add 15 to both sides..
$10x=16$
Divide both sides by 10.
$x=\frac{16}{10}=\frac{8}{5}$
