Answer
$x\approx 2.8456$
Work Step by Step
Add $2$ to both sides:
$7^x=254$
Take the natural logarithm of both sides:
$\ln{7^x}=\ln{254}$
Apply the Power Property of Logarithims:
\begin{align*}
x\cdot \log{7}&=\ln{254}\\\\
\frac{x\cdot \ln7}{\ln7}&=\frac{\ln{254}}{\ln7}\\\\
x&=\frac{\ln{254}}{\ln7}\\\\
\end{align*}
Use a calculator to evaluate:
$x\approx 2.8456$
