Change of Base Formula
Key points
- Use the change of base formula to rewrite a logarithm with another base, or to find the value of the logarithmic expression.
Change of base is the method used when evaluating the value of a logarithmic expression with a base other than 10 or e. Most calculators can only evaluate logarithms with these bases.
- The formula for a change of base is seen on the right.
- The base of the adjusted logarithm is usually 10.
- The argument is evaluated as a logarithm in the numerator.
- The base is evaluated as a logarithm in the denominator.
The example to the left shows the process of evaluating a logarithm with a base of 8 and an argument of 20.
- The value of the logarithm of the argument (20), is divided by value of the logarithm of the base (8).
- 10 is the base for both the numerator and the denominator, but is not actually written in the expression.
- You could technically use any base, but 10 and e are best for most calculators.
Subscribe to the Inertia Newsletter
IB News, Covid-19 Updates, Deadlines, Tips and Tricks, and Hundreds of Free Resources are Awaiting You!
Features
- IB Question Bank
- Thousands of IB Questions
- Practice Exams
- Detailed Answers
- Ask-A-Question System
