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: 51


$\displaystyle \frac{1}{2}\log_{4}x-3$

Work Step by Step

Basic logarithmic 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: $\log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ --- $\displaystyle \log_{4}\frac{\sqrt{x}}{64}\qquad $... apply Quotient Rule $=\log_{4}\sqrt{x}-\log_{4}64\qquad $...$\sqrt{x}=x^{1/2}, 64=4^{3}$ $=\log_{4}x^{1/2}-\log_{4}4^{3}\qquad $... apply Power Rule $=\displaystyle \frac{1}{2}\log_{4}x-\log_{4}4^{3}\qquad $... apply $\log_{b}b^{x}=x $ =$\displaystyle \frac{1}{2}\log_{4}x-3$
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