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