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: 31



Work Step by Step

With $1.5=\frac{3}{2}$, then $\ln(1.5) = \ln \left(\dfrac{3}{2} \right)$ Recall that $\ln\left(\dfrac{M}{N}\right) = \ln M-\ln N$. Using the rule above gives: $\ln \left(\dfrac{3}{2} \right) = \ln3-\ln2$ With $\ln3 = b \hspace{20pt} \text{and} \hspace{20pt} \ln2=a$, then $\ln3-\ln2 = b-a$ Therefore, $\ln1.5 = \boxed{b-a}$
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