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 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 331: 38


$\log_3 x -2$

Work Step by Step

Recall: $\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$ Using the rule above gives: $\log_3 \left(\dfrac{x}{9} \right) = \log_3 x - \log_3 9$ With $9=3^2$, then the equation above is equivalent to $\log_3{\left(\dfrac{x}{9}\right)} = \log_3{x}-\log_3{(3^2)}$ Since $\log_a a^r =r$, then the equation above simplifies to: $\log_3{\left(\dfrac{x}{9}\right)} = \log_3{x}-2$
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