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: 33

Answer

$log_{10}\frac{x^{3}-2x}{x+1}$

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, $log_{10}x-log_{10}(x+1)+log_{10}(x^{2}-2)=log_{10}\frac{x}{x+1}+log_{10}(x^{2}-2)$. 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, $log_{10}\frac{x}{x+1}+log_{10}(x^{2}-2)=log_{10}\frac{x(x^{2}-2)}{x+1}=log_{10}\frac{x^{3}-2x}{x+1}$.
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