# Change of Base Formula

Pronunciation: /tʃeɪndʒ ʌv beɪs ˈfɔɹ.mjə.lə/ Explain

The change of base formula is used to change the base of logarithms.[2] The change of base formula is .

When logarithms were first invented, there were no calculators. Mathematicians and astronomers used books published with tables of logarithms. Each table had exactly one base. To find a logarithm with another base, they used the change of base formula.

Today, most calculators and math based computer programs have logarithms in two bases: base 10 and base e. To find a logarithm in any other base, one must use the change of base formula.

### Mnemonic What is this?

 Figure 1: Change of base mnemonic.

### Examples

1. Solve log24.

Check
2. Solve log522.

Check

### References

1. McAdams, David E.. All Math Words Dictionary, change of base formula. 2nd Classroom edition 20150108-4799968. pg 32. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 113-114. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n130/mode/1up/search/base. Buy the book

### More Information

• McAdams, David E.. Logarithm. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. https://www.allmathwords.org/en/l/logarithm.html.

### Cite this article as:

McAdams, David E. Change of Base Formula. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/changeofbaseformula.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/11/2010: Added "References", "More Information". (McAdams, David E.)
11/25/2008: Initial version. (McAdams, David E.)

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