College Algebra (11th Edition)

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

Chapter 4 - Review Exercises: 65

Answer

$x=-3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \ln[\ln(e^{-x})]=\ln3 ,$ drop the $\ln$ on both sides. Then use the properties of logartihms to simplify the result. Use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since both sides have the same logarithmic base, then the logarithm can be droppped. Hence, the equation above is equivalent to \begin{array}{l}\require{cancel} \ln(e^{-x})=3 .\end{array} Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent \begin{array}{l}\require{cancel} -x\ln e=3 .\end{array} Since $\ln e=1,$ the equation above is equivalent to \begin{array}{l}\require{cancel} -x(1)=3 \\\\ -x=3 \\\\ x=-3 .\end{array}
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