Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 70

Answer

$log_{5}2$

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, $log_{5}14+log_{5}3-log_{5}21= log_{5}(14\times3)-log_{5}21= log_{5}42-log_{5}21$. 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_{5}42-log_{5}21=log_{5}\frac{42}{21}=log_{5}2$
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