Logarithm Identities

Free interactive math game: Logarithm Identities — log(1)=0, log_a(a)=1. Part of the Logarithms category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. log_5(5) = ?
  2. log_5(1) = ?
  3. log_10(10) = ?
  4. log_10(1) = ?

About this exercise

The two logarithms that hold for every base.

How to solve it

The log of 1 is always 0, and the log of the base itself is always 1.

Worked example

Log base 7 of 7 is 1, and log base 7 of 1 is 0.

Common mistake

Swapping the two. Any base to the power zero is 1, which is what fixes them.