Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 42


$x=1.099$ $x=0.693$

Work Step by Step

$e^{2x}-5e^x+6=0$ $(e^x)^2-5e^x+6=0~~$ ($a=1,b=-5,c=6$): $e^x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-(-5)±\sqrt {(-5)^2-4(1)(6)}}{2(1)}=\frac{5±\sqrt {1}}{2}=\frac{5±1}{2}$ $e^x=3$ $\ln e^x=\ln3$ $x=1.099$ $e^x=2$ $\ln e^x=\ln2$ $x=0.693$
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