The change of base formula helps us manipulate logarithmic expressions by rewriting them in bases of 10 or e. This formula involves finding the ratios between the logarithms between the original …

To change the base of a logarithm from base ‘a’ to base ‘c’, use the change of base formula: loga(b)= [logc(b)]/ [logc(a)]. For example, log3(81) written in base 5 is log5(81)/log5(3).

The Change of Base Formula is a formula for converting a log expression from one base (usually one that you can't plug into your calculator) to a log-fraction expression with a different base (usually the …

Jul 23, 2025 · Formula for Base Change of Log This formula expresses a logarithm of a number with a particular base as a ratio of two logarithms, each with a different base than the original logarithm.

The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.

Learn how to rewrite any logarithm using logarithms with a different base. This is very useful for finding logarithms in the calculator!

Nov 6, 2024 · This page covers all 8 log rules (including the change of base formula and log exponent rules). Each log rule is covered in-depth with simple explanations and examples.

Many calculators have only functions for calculating base-10 and base-e logarithms. But you can still calculate logs in other bases, you just need to use the change of base formula to put in in base 10.

Learn how to apply the change-of-base formula for logs, explore how to use it to simplify your log equations, and how you can derive the change-of-base formula.

In this beginner-friendly lesson, we explore the Change of Base Formula in Logarithms step-by-step.