# Log Graphs

Recall that e=2.718 to 3 decimal places and logs can be thought of as powers. See more on e or more on logs.

This diagram shows the graphs of $y=e^x$ and $y=\ln(x)$

The natural log, $\ln(x)$, is the log that has base e – it can also be written as $\log_e(x)$.

$\ln(x)$ is the inverse of $e^x$ and so these graphs are reflections of each other in the line y=x.

Since $\ln(x)$ and $e^x$ are mathematical inverses we have that

$\ln\left(e^x\right)=e^{\ln(x)}=x$