What is it about the number e that makes it so that taking log to the base e is called the natural logarithm?
In: Mathematics
I’m not sure why it’s called natural, but the reason e is special is because with exponetiation it is equal to its own derivative.
So for f(x)= e^x
then f'(x) = e^x
with doesn’t seem that useful
But since for any number (by simple exponetiation rules)
a = e^ln(a)
but then for f(x) = a^x = e^ln(a)x
and then by a simple chain rule then
f'(x) = ln(a)e^ln(a)x = ln(a)a^x
making e a very useful constant.
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