Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 826: 97

Answer

$x=1$

Work Step by Step

$\log x=\ln x$ Write the RHS using change-of-base (to base 10) $\displaystyle \log x=\frac{\log x}{\log e}$ $\displaystyle \log x-\frac{\log x}{\log e}=0$ $\displaystyle \log x(1-\frac{1}{\log e})=0$ Since $(1-\displaystyle \frac{1}{\log e})\neq 0$, it must be that $\log x=0$. That is, $\quad x=1.$ ALTERNATIVELY, Graphing approach: Graph $y=\log x$ and $y=\ln x$ on the same coordinate system. The only intersection point is (1,0), thus, $x=1.$
Small 1566519014
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.