Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 16

Solve for $x$ in the equation $\displaystyle \ln(1 + e^{-x}) = 3$


$
\begin{equation}
\begin{aligned}

\ln(1 + e^{-x}) =& 3
\\
\\
e^{\ln (1 + e^{-x})} =& e^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)

\end{aligned}
\end{equation}
$