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December 12th, 2017, 09:34 AM   #11
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The first principles approach would be to solve the functional equation $$f(xy)=f(x)+f(y)$$
You have to arbitrarily pick one of the solutions, but the choice of $f'(1)$ is reasonably natural and gives you a definition of $e$.

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December 12th, 2017, 03:14 PM   #12
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How would you solve that "from first principles"?
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December 12th, 2017, 06:12 PM   #13
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The link contains a derivation.
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