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: 30


$ a-b$

Work Step by Step

Recall: $\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$ Using the rule above gives: $\ln \left(\dfrac{2}{3} \right) = \ln2-\ln3$ With $\ln3 = b \hspace{20pt} \text{and} \hspace{20pt} \ln2=a$, then $\ln2-\ln3 = a-b$ Therefore $\ln \left(\dfrac{2}{3} \right) = \boxed{a-b}$
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