# What’s so “natural” about the base of natural logarithms?

There are so many available bases. Why is the strange number $e$ preferred over all else?

Of course one could integrate $\frac{1}x$ and see this. But is there more to the story?

$e^x$ has the two following nice properties
If we looked at $a^x$ instead, we would get:
So $e$ is vital to the integration and differentiation of exponentials.