Answer
$m=\dfrac{e^8-3}{2}$
Work Step by Step
Recall:
$$\ln{a}=y \longleftrightarrow e^y=a$$
Use the definition above to obtain:
\begin{align*}
\ln{\left(2m+3\right)}&=8\\\\
e^8&=2m+3\\\\
e^8-3&=2m\\\\
\frac{e^8-3}{2}&=m
\end{align*}
Check:
\begin{align*}
\ln{\left(2\left(\frac{e^8-3}{2}\right)+3\right)}&\stackrel{?}=8\\\\
\ln{\left(e^8-3+3\right)}&\stackrel{?}=8\\\\
\ln{\left(e^8\right)}&\stackrel{?}=8\\\\
8&\stackrel{\checkmark}=8\end{align*}
