Logarithm Power Rule

Free interactive math game: Logarithm Power Rule — log(xⁿ). 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_3(3^3) = ?
  2. log_3(9^2) = ?
  3. log_3(3^2) = ?
  4. log_5(5^3) = ?

About this exercise

The logarithm of a number raised to a power.

How to solve it

The exponent comes out in front and multiplies the logarithm, because a power is repeated multiplication and logarithms turn multiplication into addition.

Worked example

Log base 5 of 5 squared is 2 times log base 5 of 5, that is 2 x 1 = 2.

Common mistake

Raising the logarithm to the power instead. The exponent multiplies the result, it does not act on it a second time.