Intermediate Algebra (6th Edition)

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

Chapter 9 - Sections 9.1-9.6 - Integrated Review - Functions and Properties of Logarithms - Page 580: 34

Answer

$log_{2}\frac{(x^{2}-3x)}{(x^{2}+4)}$

Work Step by Step

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, $log_{2}x+log_{2}(x-3)-log_{2}(x^{2}+4)= log_{2}x(x-3)-log_{2}(x^{2}+4)= log_{2}(x^{2}-3x)-log_{2}(x^{2}+4)$. 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_{2}(x^{2}-3x)-log_{2}(x^{2}+4)= log_{2}\frac{(x^{2}-3x)}{(x^{2}+4)}$.
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