Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 811: 83



Work Step by Step

$x^{8}-y^{8}$ is a difference of squares, $x^{8}-y^{8}=(x^{4}-y^{4})(x^{4}+y^{4})$ $x^{4}-y^{4}$is a difference of squares, $x^{8}-y^{8}=(x^{2}+y^{2})(x^{2}-y^{2})(x^{4}+y^{4})$ Applying the rule: $\log_{a}(MN)=\log_{a}M+\log_{a}N$ $\log_{a}(x^{8}-y^{8})=\log_{a}[(x^{2}-y^{2})(x^{2}+y^{2})]+\log_{a}(x^{2}+y^{2})$ So, $\log_{a}(x^{8}-y^{8})-\log_{a}(x^{2}+y^{2})=\log_{a}[(x^{2}-y^{2})(x^{4}+y^{4})]$ $=\log_{a}[x^{6}-x^{4}y^{2}+x^{2}y^{4}-y^{6}]$
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