Logarithm of a Root

Free interactive math game: Logarithm of a Root — log₄(√4) = 1/2. 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_4(√4) = ?
  2. log_9(⁴√9) = ?
  3. log_4(⁴√4) = ?
  4. log_25(√25) = ?

About this exercise

Logarithms of roots.

How to solve it

Rewrite the root as a fractional exponent, then bring that exponent out in front of the logarithm.

Worked example

For the square root of 8 in base 2, the logarithm is half of 3, which is 1.5.

Common mistake

Ignoring the root. A square root halves the logarithm and a cube root takes a third of it.