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.
 Figure 1: Change of base mnemonic. 


Examples
 Solve log_{2}4.
Check
 Solve log_{5}22.
Check
References
 McAdams, David E.. All Math Words Dictionary, change of base formula. 2nd Classroom edition 201501084799968. pg 32. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 113114. 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.
Image Credits
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.)