Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.6 - Properties of Logarithms - Exercise Set: 27

Answer

$log_{5}(x^{3}z^{6})$

Work Step by Step

We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number). Therefore, $3log_{5}x+6log_{5}z =log_{5}x^{3}+log_{5}z^{6}$. We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{5}x^{3}+log_{5}z^{6}=log_{5}(x^{3}\times z^{6})=log_{5}(x^{3}z^{6})$.
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