Solve log_x(64) = 3.

Explanation

• Turn the log into index form first: log_x(64) = 3 means x³ = 64.
• The cube root of 64 is 4, so x = 4.
• The unknown here is the base of the logarithm. The value of the logarithm is already given as 3.
• A logarithm base must be positive and cannot equal 1, which rules out several bases immediately.
• Prime factorising helps in harder versions of this question: 64 = 2⁶, and 2⁶ = (2²)³ = 4³.