Different definitions of logarithm: Index

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 f(x) = \displaystyle \int_1^x \frac{dt}{t} satisfies the four statements.

Part 8: Computation of standard integrals and derivatives involving logarithmic and exponential functions.

 

 

 

 

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2 Comments

  1. Proving theorems and special cases (Part 13): Uniqueness of logarithms | Mean Green Math
  2. Proving theorems and special cases (Part 16): An old homework problem | Mean Green Math

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