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 - Page 881: 50

Answer

$2log_{3}x+log_{3}(x-9)$

Work Step by Step

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, $log_{3}x^{2}(x-9)=log_{3}x^{2}+log_{3}(x-9)$. 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, $log_{3}x^{2}+log_{3}(x-9)=2log_{3}x+log_{3}(x-9)$.
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