My Math Forum lnx and e^x

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 December 12th, 2017, 10:34 AM #11 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,112 Thanks: 2369 Math Focus: Mainly analysis and algebra 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 $e$. The Glorious Logarithm
 December 12th, 2017, 04:14 PM #12 Global Moderator   Joined: Dec 2006 Posts: 18,408 Thanks: 1459 How would you solve that "from first principles"?
 December 12th, 2017, 07:12 PM #13 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,112 Thanks: 2369 Math Focus: Mainly analysis and algebra The link contains a derivation.

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