Answer
$\displaystyle \{\frac{\ln\pi}{1+\ln\pi}\}$ or $\{0.534\}$
Work Step by Step
... Apply $\ln$(...) to both sides and isolate x
$\ln\pi^{1-x}=\ln e^{x}$
$(1-x)\ln\pi=x$
$\ln\pi-x\ln\pi=x$
$\ln\pi=x+x\ln\pi$
$\ln\pi=x(1+\ln\pi)$
$x=\displaystyle \frac{\ln\pi}{1+\ln\pi}\approx 0.534$
The solution set is $\displaystyle \{\frac{\ln\pi}{1+\ln\pi}\}$ or $\{0.534\}$
