Answer
$$x =\ln\frac{1}{e^3-1}$$
Work Step by Step
Given $$\ln (1+e^{-x})=3$$
Then
\begin{align*}
\ln (1+e^{-x})&=3\\
1+e^{-x}&=e^3\\
e^{-x}&=e^3-1\\
\ln e^{-x}&=\ln (e^3-1)\\
-x&=\ln (e^3-1)\\
x&=\ln (e^3-1)^{-1}\\
&=\ln\frac{1}{e^3-1}
\end{align*}