Logarithm of a Fraction

Free interactive math game: Logarithm of a Fraction — log₂(1/8) = -3. 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(1/4) = ?
  2. log_3(1/9) = ?
  3. log_3(1/81) = ?
  4. log_2(1/2) = ?

About this exercise

Logarithms of numbers below one.

How to solve it

A fraction is a negative power of the base, so its logarithm is negative.

Worked example

In base 2 the log of one eighth is -3, because 2 to the power -3 is one eighth.

Common mistake

Losing the minus sign. Any value under 1 gives a negative logarithm.