Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set - Page 475: 64

Answer

$\log_{4}\sqrt[3]{\frac{x}{y}}$

Work Step by Step

$\displaystyle \frac{1}{3}(\log_{4}x-\log_{4}y)=\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$ $=\displaystyle \frac{1}{3}\cdot\log_{4}(\frac{x}{y}) \quad $...apply the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$ $=\displaystyle \log_{4}(\frac{x}{y})^{1/3}=\log_{4}\sqrt[3]{\frac{x}{y}}$
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