Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 38

Answer

$\log_3{x}-2$

Work Step by Step

Recall: (1) $\sqrt[m]{a}=a^{\frac{1}{m}}$ (2) $\log_a {x^n}=n\cdot \log_a {x}$. (3) $\log_a{xy}=\log_a{x} +\log_a{y}$ (4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$ Use Rule (4) above to obtain: $\log_3 {\frac{x}{9}}=\log_3 {x}-\log_3 {9}.$ Use Rule (2) above to obtain: $\log_3 {x}-\log_3 {9}\\ =\log_3 {x}-\log_3 {3^2}\\ =\log_3 {x}-2\cdot \log_3 {3}\\ =\log_3{x}-2\cdot1\\ =\log_3{x}-2$
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.