Simplify Logarithm Expression

Free interactive math game: Simplify Logarithm Expression — log(x) + log(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. 3 · log_3(27) = ?
  2. log_2(16) − log_2(2) = ?
  3. 4 · log_3(27) = ?
  4. 4 · log_5(125) = ?

About this exercise

Combining several logarithm terms into one.

How to solve it

Use the product, quotient and power rules to fold everything into a single logarithm, then evaluate it.

Worked example

Log of 4 plus log of 8 to base 2 is the log of 32, which is 5.

Common mistake

Applying a rule with mismatched bases. All the rules require the same base throughout.