What gives the natural logarithm its name? What's "natural" about it?
I know that the natural logarithm is defined as $\ln(x)$ or $\log_{e}(x)$, where $e$ is the Euler number.
But what is so "natural" about it? Is there an explanation on why that name was chosen?
Solution 1:
Base $e$ for exponentials and logarithms is distinguished by the fact that it is the unique base $c$ such that the derivative of $f(x)=c^x$ at $x=0$ is equal to one.