Answer
$\displaystyle \{\frac{3}{\ln\pi-1}\}$ or $\{20.728\}$
Work Step by Step
... Apply $\ln$(...) to both sides and isolate x
$\ln e^{x+3}=\ln\pi^{x}$
$ x+3=x\ln\pi$
$3=x\ln\pi-x$
$3=x(\ln\pi-1)$
$x=\displaystyle \frac{3}{\ln\pi-1}\approx 20.728$
The solution set is $\displaystyle \{\frac{3}{\ln\pi-1}\}$ or $\{20.728\}$
