Answer
$x=\dfrac{3}{\ln{\pi}-1} \approx 20.728$
Work Step by Step
To find the value of $x$, we apply $\log$ to both sides and then isolate $x$ as follows:
$$\ln \left(e^{x+3}\right)=\ln \left(\pi^{x}\right)$$
Use the logarithmic properties: $\log m^n= n \log m\quad$ and $\quad \ln{e} = 1$ to obtain:
\begin{align*}(x+3)\cdot \ln{e}&=x \cdot \ln\pi \\
(x+3)(1)&=x\cdot \ln{\pi}\\
x+3&=x \cdot \ln\pi\\\
3&=x\cdot \ln{\pi}-x\\
3&=x(\ln\pi-1) \\
\dfrac{3}{\ln{\pi}-1}&=x\\
20.728&\approx x\end{align*}
Thus, our answer is: $x =\dfrac{3}{\ln{\pi}-1}\approx 20.728$
