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: 12

Answer

$\text{false}$

Work Step by Step

Note that $$\dfrac{\ln 8}{\ln 4}=\dfrac{\ln 2^{3}}{\ln 2^{2}}$$ Using the rule $\ln a^{m}=m \ln a$ yields $$\require{cancel}\dfrac{\ln 8}{\ln 4}=\dfrac{3 \ln 2}{2 \ln 2}=\dfrac{3 \cancel{\ln 2}}{2 \cancel{\ln 2}}=\dfrac{3}{2}$$ Therefore $$\dfrac{\ln 8}{\ln 4}=\frac{3}{2}\ne2$$ The given statement is false.
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