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Change of Base Rule for Logarithms

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Videos, worksheets, solutions, and activities to help Algebra students learn about the change of base rule in logarithms.
How to determine the value of any logarithm using the change of base formula?

What is the Change of Base Formula?

The Change of Base Formula states that

\({\log _a}x = \frac{{{{\log }_b}x}}{{{{\log }_b}a}}\)

where a, b and x are positive real numbers such that a ≠ 1 and b ≠ 1

When we encounter logarithms with bases not of the common or natural logarithm, we often need the change of base formula. The change of base formula allows us to convert a logarithm from one base to another. By using the change of base formula, we can change a logarithmic term to allow us to input it into a calculator. Most calculators only accept logarithms of base 10 or base e.

This video shows how to determine the value of any logarithm using the change of base formula.
How to use the change of base formula for logs to evaluate a logarithmic statement.

This video shows the change of base formula for logarithms, and do a few examples of evaluating logarithms using the formula and a calculator.
Change the base of Logarithm

Change of Base Formula
The Change of Base Formula for logarithms, including the proof.
Change of base formula
A discussion and the derivation of the formula for changing the base of logarithms.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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