Cambridge O Level Additional Mathematics · Syllabus 4037 · Logarithmic and Exponential Functions
Change of Base Law
What is Change of Base Law?
The rule that rewrites a logarithm in one base as a quotient of logarithms in any other valid base: log to base a of b equals log to base c of b divided by log to base c of a, for bases a and c that are positive and not equal to one and for a positive argument b. Choosing c equal to e gives log to base a of b as the natural logarithm of b divided by the natural logarithm of a, and choosing c equal to ten gives the same value using common logarithms. It is what allows a calculator that offers only ln and lg to evaluate a logarithm to any base, and it allows an equation containing two different bases to be rewritten in a single base.
This definition is part of the Logarithmic and Exponential Functions chapter in Cambridge O Level Additional Mathematics.