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: 34

Answer

$log_{10}\frac{4x^{4}+4x}{x-3}$

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, $log_{9}(4x)-log_{9}(x-3)+log_{9}(x^{3}+1)=log_{9}\frac{4x}{x-3}+log_{9}(x^{3}+1)$. 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, $log_{9}\frac{4x}{x-3}+log_{9}(x^{3}+1)=log_{10}\frac{4x(x^{3}+1)}{x-3}=log_{10}\frac{4x^{4}+4x}{x-3}$.
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