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It's not a weird base, it's really the most natural base to choose, which is why it's called the natural logarithm. It doesn't particularly matter what base you choose, because you can always convert from one base to another, but often the natural logarithm is simpler to work with. For example, the derivative of ln(x) is just 1/x. The derivative of log10(x) is 1/(x*ln(10)).
This is because ln(x) is the inverse of e^x, which has the unique property that it is its own derivative.
The simple derivative really is nice, thanks for pointing this out!