Answer
$x=\frac{3}{2}$
Work Step by Step
We are given that $5^{2x}=125$. Both of these numbers are powers of 5, so we can rewrite the equation as $5^{2x}=5^{3}$.
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, $2x=3$. To solve for x, divide both sides by 2.
$x=\frac{3}{2}$
