Answer
$x=0.75$
Work Step by Step
\begin{align*}
\log{\left(25^{2x}\right)}&=\log{125} &\text{Take the common logarithm of both sides.}\\\\
2x\cdot \log{25}
&=\log{125} &\text{Apply the Power Property of Logarithms.}\\\\
\dfrac{2x\cdot\log{25}}{2\log{25}}&=\dfrac{\log{125}}{2\log{25}} &\text{Divide $2\log{25}$ to both sides.}\\\\
x&= \dfrac{\log{125}}{2\log{25}}\\\\
x&=0.75 &\text{Use a calculator to evaluate.}
\end{align*}
