Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.6 - Properties of Logarithms - Exercise Set: 30

Answer

$log_{6}6$

Work Step by Step

We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{6}21+log_{6}2-log_{6}7=log_{6}(21\times2)-log_{6}7=log_{6}42-log_{6}7$. We know 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, $log_{6}42-log_{6}7=log_{6}\frac{42}{7}=log_{6}6$.
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