Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 321: 34



Work Step by Step

Note that $y=\log_a x \text{ is equivalent to } x= a^y$. Thus, if $y = \log_{\sqrt{3}} 9 \hspace{5pt},$ then $\hspace{5pt}(\sqrt{3})^y=9$ Since $9=3^2=(\sqrt{3})^4$, then $(\sqrt{3})^y=(\sqrt{3})^4$ Use the rule $a^m=a^n \implies m=n$ to obtain: $y=4$ Therefore, $ \log_{\sqrt{3}} 9 = \boxed{4}$
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