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: 37


a.) $x = e^3$ b.) $x = 2$

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\ln x = 3$ b.) $\ln e^2 = x$ a.) $\ln x = 3$ 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] $\ln x = 3 \rightarrow e^3 = x$ $x = e^3$ b.) $\ln e^2 = x$ Bring the square to the front of the logarithm $2\ln e = x$ $2\times1 = x$ [Note: $\ln e = 1$] $x = 2$
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