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: 51

Answer

$2log_{6}x-log_{6}(x+3)$

Work Step by Step

We know that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{6}\frac{x^{2}}{x+3}=log_{6}x^{2}-log_{6}(x+3)$. 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, $log_{6}x^{2}-log_{6}(x+3)=2log_{6}x-log_{6}(x+3)$.
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