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: 41

Answer

$ log_{4}5-log_{4}9-log_{4}z $

Work Step by Step

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, $log_{4}\frac{5}{9z}=log_{4}5-log_{4}9z$. 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_{4}5-(log_{4}9z)= log_{4}5-(log_{4}9+log_{4}z)= log_{4}5-log_{4}9-log_{4}z $.
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