College Algebra (11th Edition)

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

Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises: 35

Answer

$x=e^2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 5\ln x=10 ,$ convert it to exponential form. $\bf{\text{Solution Details:}}$ Dividing both sides by $ 5 ,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \ln x=\dfrac{10}{5} \\\\ \ln x=2 .\end{array} Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e x=2 .\end{array} Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} e^2=x \\\\ x=e^2 .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.