College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.4 - Evaluating Logarithms and the Change-of-Base Theorem - 4.4 Exercises: 48

Answer

$-4$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of logarithms to evaluate the given expression, $ \ln\left( \dfrac{1}{e^4} \right) .$ $\bf{\text{Solution Details:}}$ Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \ln1-\ln e^4 .\end{array} Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \ln1-4\ln e .\end{array} Since $\ln e=1$ and $\ln1=0,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 0-4(1) \\\\= -4 .\end{array}
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