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 1x and see this. But is there more to the story?

Answer

Differentiation and integration is precisely why it is considered natural, but not just because
1xdx=lnx

ex has the two following nice properties

ddxex=ex

exdx=ex+c

If we looked at ax instead, we would get:

ddxax=ddxexln(a)=ln(a)ax

axdx=exln(a)dx=axln(a)+c

So e is vital to the integration and differentiation of exponentials.

Attribution
Source : Link , Question Author : Community , Answer Author : draks …

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