Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of $e^x$, a strange enough exponent already.
But there’s a fresh, intuitive explanation: The natural log gives you the time needed to reach a certain level of growth. Demystifying the Natural Logarithm (ln) by Kalid Azad
Some things go up really fast, like the number of cases of coronavirus in March. Some things go down really fast, like the stock market in March.
Logarithms are a way to flatten exponential curves, so we can see and understand their structure, even when dealing with extreme/exponential growth.