Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 335: 86

Answer

a. 5 b. e

Work Step by Step

$\displaystyle \int_{1}^{x}\frac{1}{t}dt=$ Log Rule = $\ln|t|_{1}^{x}$ $= \ln|x|-\ln 1$ the integral bounds suggest $x > 1 > 0$, so we write $=\ln x$ a. $\ln x=\ln 5\qquad $/... apply $e^{(..)}$ to both sides $x=5$ b. $\ln x=1\qquad $/... apply: $\ln e =1$ $\ln x=\ln e\qquad $/... apply $e^{(..)}$ to both sides $x=e$
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