Change-of-Base Rule

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How to Solve Logarithms Using the Change-of-Base Rule

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Description

 

A detailed tutorial on solving logarithms with the change-of-base rule. Step by step tutorial including several examples of how to solve logarithms using the change-of-base rule for reference.

 

Overview

 

The change-of-base rule is typically only used when solving logarithms with a calculator. It allows you to use a number besides the calculator presets. Tha change-of-base rule states that:

\log_b{x} = \frac{\log_k{x}}{\log_k{b}}.

In this formula, b must not be equal to one, as the logarithm of one is simply zero. This formula also implies that all logarithms are similar to each other.


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