Answer
$\dfrac{\log_{10} {0.375}+7}{2}$
Work Step by Step
Divide $8$ to both sides of the equation to obtain:
$10^{2x-7}=\dfrac{3}{8}$
$10^{2x-7}=0.375$
$\because a^y = x \text{ is equivalent to } \log_a x = y$
$\therefore 10^{2x-7}=0.37\implies \log_{10} 0.375=2x-7$
Solve the equation above to obtain:
\begin{align*}
2x-7&=\log_{10} {0.375}\\\\
2x&=\log_{10} {0.375}+7\\\\
x&=\dfrac{\log_{10} {0.375}+7}{2}
\end{align*}
