Change of Base Formula

Free interactive math game: Change of Base Formula — log(b) / log(a). 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. Rewrite using change of base formula (using base 10): log_3(8) = ?
  2. Rewrite using change of base formula (using base 10): log_5(18) = ?
  3. Rewrite using change of base formula (using base 10): log_5(11) = ?
  4. Rewrite using change of base formula (using base 10): log_2(3) = ?

About this exercise

Rewriting a logarithm in a different base.

How to solve it

Divide the logarithm of the value by the logarithm of the old base, both taken in the new base.

Worked example

Log base 4 of 16 becomes log base 2 of 16 divided by log base 2 of 4, that is 4 : 2 = 2.

Common mistake

Subtracting the logarithms. The change-of-base rule uses division.