Graphing Natural Logarithmic Functions

The inverse function of $ y=e^x $ is $ y=\log_{e}{x} $. Therefore $ y=\log_{e}{x} $ is an inverse function, it is a reflection of $ y=e^x $ in the line $ y=x $.

The graphs of $y=e^x$ is $y=\log_{e}{x}$:

\begin{array}{|c|c|c|} \require{AMSsymbols} \require{color} \hline
& y=e^x & \color{red}y =\log_{e}{x} \\ \hline
\text{domain} & x \in \mathbb{R} & \color{red}x \gt 0 \\ \hline
\text{range} & y \gt 0 & \color{red}y \in \mathbb{R} \\ \hline
\text{asymptote} & horizontal\ y=0 & \color{red}vertical\ x=0 \\ \hline
\text{fixed point} & (0,1) & \color{red}(1,0) \\ \hline
\end{array}