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: 34


$\displaystyle \frac{1}{3}\log_{b}x+4\log_{b}y-5\log_{b}z $

Work Step by Step

$\displaystyle \log_{b}\frac{\sqrt[3]{x}y^{4}}{z^{5}}=\log_{b}\frac{x^{1/3}y^{4}}{z^{5}}$ $\quad $..apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$ $=\log_{b}x^{1/3}+\log_{b}y^{4}-\log_{b}z^{5}$ $\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ $=\displaystyle \frac{1}{3}\log_{b}x+4\log_{b}y-5\log_{b}z $
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