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Change of base formula

Revision as of 21:29, 10 February 2009 by Duelist (talk | contribs) (New page: The change of base formula, shown below, is a property of logarithms. It states that for any positive <math>d,a,b</math> such that none of <math>d,a,b</math> are <math>1</math>, we have: ...)
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The change of base formula, shown below, is a property of logarithms. It states that for any positive $d,a,b$ such that none of $d,a,b$ are $1$, we have:

\[\log_a b = \frac{\log_d b}{\log_d a}\]

It is called the change of base formula because $\log_a b$ can be expressed as a quotient of logarithms of any base $d$. For example, when approximating logarithms with calculators, we use the change of base formula when $d=e$ so we can use the natural log key on the calculator.

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