Compare Logarithms

Free interactive math game: Compare Logarithms — log₂(8) vs log₃(27). 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. Which is greater? log_10(10) or log_10(1000)
  2. Which is greater? log_10(100) or log_2(32)
  3. Which is greater? log_5(25) or log_5(25)
  4. Which is greater? log_5(5) or log_2(64)

About this exercise

Comparing two logarithms.

How to solve it

Evaluate each one if you can. Otherwise remember that a larger value gives a larger logarithm within the same base.

Worked example

Comparing log base 2 of 16 with log base 3 of 27 gives 4 against 3, so the first is larger.

Common mistake

Comparing by the size of the numbers inside. Different bases make that unreliable.