Precalculus (6th Edition) Blitzer

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

Chapter 3 - Review Exercises - Page 513: 50


$2+3\log_{6}x $

Work Step by Step

Basic logarihmic properties:$ \left\{\begin{array}{l} \log_{b}1=0\\ \log_{b}b=1\\ \log_{b}b^{x}=x\\ b^{\log_{b}}x=x \end{array}\right.$ Rules: The Product Rule: $\log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$ The Quotient Rule: $\displaystyle \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$ The Power Rule: $\log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ --- $\log_{6}(36\cdot x^{3})=\qquad $... apply Product Rule $=\log_{6}36+\log_{6}x^{3}=\qquad $... recognize 36 as $6^{2}$ $=\log_{6}6^{2}+\log_{6}x^{3}=\qquad $... apply Power Rule $=2\log_{6}6+3\log_{6}x=\qquad $... apply $\log_{b}b=1$ $=2\cdot 1+3\log_{6}x $ = $2+3\log_{6}x $
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