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Change of Base Formula

A formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.

 

Assume that x, a, and b are all positive. Also assume that a ≠ 1, b ≠ 1.

Change of base formula:

 

Example 1:

 

Example 2:    (note that )

 

Example 3:

 

See also

Logarithm rules, common logarithm, natural logarithm

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes