Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 26


$x=\dfrac{1}{e^2-1} \approx 0.157$

Work Step by Step

Apply the logarithmic property: $\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$ and rearrange the given expression to obtain: $\ln \left(\dfrac{x+1}{x} \right) = 2$ or, $e^2 =\dfrac{x+1}{x}$ or, $e^2 \ x=x+1$ or, $x(e^2-1)=1$ or, $x=\dfrac{1}{e^2-1}$ Thus, our answer is: $x=\dfrac{1}{e^2-1} \approx 0.157$
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