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: 30



Work Step by Step

NOoe that $y=\log_a x \text{ is equivalent to } x= a^y$ Thus, if $y = \log_{1/3} 9$, then $\left(\dfrac{1}{3}\right)^y=9$ Since $9=3^2=\left(\dfrac{1}{3}\right)^{-2},$ then $\left(\dfrac{1}{3}\right)^y=\left(\dfrac{1}{3}\right)^{-2}$ Use the rule $a^m=a^n \implies m=n$ to obtain: $y=-2$ Therefore, $ \log_{1/3} 9 = \boxed{-2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.