Changing the Base

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Changing the Base

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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 © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Changing the Base

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

\

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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