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 - Page 578: 32

Answer

$log_{8}\frac{15}{4}$

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, $log_{8}5+log_{8}15-log_{8}20= log_{8}(5\times15)-log_{8}20= log_{8}75-log_{8}20$. 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_{8}75-log_{8}20=log_{8}\frac{75}{20}= log_{8}\frac{15}{4}$.
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