Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 38

Answer

a.) $x = \frac{1}{e}$ b.) $x = -1$

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\ln x = -1$ b.) $\ln (\frac{1}{e}) = x$ a.) $\ln x = -1$ Rewrite the natural log form to exponential form: $\ln a = b \rightarrow e^b = a$ [Note: e stands for euler's number, NOT a variable] $$\ln x = -1 \rightarrow e^{-1} = x$$ $$x = \frac{1}{e}$$ b.) $\ln (\frac{1}{e}) = x$ Rewrite the natural log form to exponential form: $\ln a = b \rightarrow e^b = a$ [Note: e stands for euler's number, NOT a variable] $$ \ln (\frac{1}{e}) = x \rightarrow e^x = \frac{1}{e}$$ Rewrite $\frac{1}{e}$ to $e^{-1}$ $$e^x = e^{-1}$$ $$x = -1$$
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