Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.6 - Properties of Logarithms - Exercise Set: 33

Answer

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

Work Step by Step

The quotient property of logarithms tells us 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, $log_{10}x-log_{10}(x+1)+log_{10}(x^{2}-2)= log_{10}\frac{x}{(x+1)}+log_{10}(x^{2}-2)$. The product property of logarithms tells us 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+1)}\times(x^{2}-2)= log_{10}\frac{x(x^{2}-2)}{(x+1)}= log_{10}\frac{(x^{3}-2x)}{(x+1)}$.
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