Answer
$x\approx4.6542$
Work Step by Step
\begin{align*}
\log{\left(7^{x-3}\right)}&=\log{25} &\text{Take the common logarithm of both sides.}\\\\
(x-3)\cdot \log{7}
&=\log{25} &\text{Apply the Power Property of Logarithms.}\\\\
\dfrac{(x-3)\cdot\log{7}}{\log{7}}&=\dfrac{\log{25}}{\log{7}} &\text{Divide $\log{7}$ to both sides.}\\\\
x-3&= \dfrac{\log{25}}{\log{7}}\\\\
x&=3+ \dfrac{\log{25}}{\log{7}} &\text{Add 3 to both sides.}\\\\
x&\approx 4.6542&\text{Use a calculator to evaluate.}
\end{align*}
