College Algebra (11th Edition)

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

Chapter 4 - Review Exercises: 53

Answer

$x=e^{\frac{13}{3}}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3\ln x=13 ,$ use the properties of equality to isolate the $\ln$ expression. Then use the definition of the natural logarithms and convert to exponential form. Finally, use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality to isolate the $\ln$ expression results to \begin{array}{l}\require{cancel} \dfrac{3\ln x}{3}=\dfrac{13}{3} \\\\ \ln x=\dfrac{13}{3} .\end{array} Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e x=\dfrac{13}{3} .\end{array} Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to \begin{array}{l}\require{cancel} x=e^{\frac{13}{3}} .\end{array}
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