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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 $ a$ to $ b$ :

$\displaystyle \log_b(x) = \frac{\log_a(x)}{\log_a(b)}
$

Thus, to change the base from $ a$ to $ b$ , divide by the log base $ a$ of $ b$ .


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-10-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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