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: 31

Answer

$log_{7}\frac{9}{2}$

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, $log_{7}6+log_{7}3-log_{7}4= log_{7}(6\times3)-log_{7}4= log_{7}18-log_{7}4$. 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_{7}18-log_{7}4=log_{7}\frac{18}{4}=log_{7}\frac{9}{2}$.
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