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: 58


$\log_3{\left(\dfrac{u^2}{v} \right)}$

Work Step by Step

Recall: $\log_a M^r = r \log_a M$ Use the rule above to obtain: $2 \log_3 u = \log_3 u^2$ Thus, $2 \log_3 u -\log_3 v = \log_3 u^2 - \log_3 v$ With $\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$, then: $2 \log_3 u -\log_3 v = \boxed{\log_3 \left(\dfrac{u^2}{v} \right)}$
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