Logarithm Quotient Rule

Free interactive math game: Logarithm Quotient Rule — log(x / y). 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_2(16 / 2) = ?
  2. log_3(81 / 9) = ?
  3. log_2(16 / 8) = ?
  4. log_3(243 / 3) = ?

About this exercise

The logarithm of one number divided by another.

How to solve it

Subtract the logarithm of the bottom from the logarithm of the top. Division inside the logarithm becomes subtraction outside it.

Worked example

Log base 2 of 64 over 8 is log of 64 minus log of 8, that is 6 - 3 = 3.

Common mistake

Reversing the order. Subtraction is not symmetric, so the numerator log always comes first.