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Changing the Base

By definition, $ x = b^{\log_b(x)}$. Taking the log base $ a$ of both sides gives

$\displaystyle \log_a(x) = \log_b(x) \log_a(b)
$

which tells how to convert the base from $ b$ to $ a$, that is, how to convert the log base $ b$ of $ x$ to the log base $ a$ of $ x$. (Just multiply by the log base $ a$ of $ b$.)


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[How to cite this work] [Order a printed hardcopy]

``Mathematics of the Discrete Fourier Transform (DFT), with Music and Audio Applications'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]