I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on how the different definitions of logarithm are in fact equivalent.
Part 1: Introduction to the two definitions: an antiderivative and an inverse function.
Part 2: The main theorem: four statements only satisfied by the logarithmic function.
Part 3: Case 1 of the proof: positive integers.
Part 4: Case 2 of the proof: positive rational numbers.
Part 5: Case 3 of the proof: negative rational numbers.
Part 6: Case 4 of the proof: irrational numbers.
Part 7: Showing that the function satisfies the four statements.
Part 8: Computation of standard integrals and derivatives involving logarithmic and exponential functions.