Answer
$a\approx 49.598$
Work Step by Step
Given \begin{equation}
\ln (a+5)=4.
\end{equation} This is a logarithmic equation. The solution steps are shown below.
\begin{equation}
\begin{aligned}
\ln (a+5) & =4\\
e^{\ln (a+5)} &= e^{4}\\
a+5 & = e^{4}\\
a&= e^{4}-5\\
a & \approx 49.598.
\end{aligned}
\end{equation} The solution is $a\approx 49.598$.