# How do you write ln(13) in exponential form?

If $x = \ln \left(13\right)$, then ${e}^{x} = 13$ is the exponential form.
In general, the equations $x = {\log}_{b} \left(y\right)$ and ${b}^{x} = y$ are equivalent (it's assumed that $b > 0$, $b \ne 0$, and $y > 0$ here).
${b}^{x} = y$ is the exponential form of $x = {\log}_{b} \left(y\right)$ and $x = {\log}_{b} \left(y\right)$ is the logarithmic form of ${b}^{x} = y$.