Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Review Exercises - Page 512: 21


$\log_{3} (-9)$ can not be evaluated.

Work Step by Step

$\log_{b}x=y $ is equivalent to $ b^{y}=x $ --- $\log_{3} (-9)=y \quad $ is equivalent to $ \quad 3^{y}=-9$ But, $ \quad 3^{y}$ is never negative, so $\log_{3} (-9)$ can not be evaluated. Alternatively, arrive to the same conclusion like this: $\log_{3}x $ is defined only for positive x. $-9$ is not in the domain of $\log_{3}x $, which is why $\log_{3} (-9)$ can not be evaluated.
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