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: 19


$x_1=2$ and $x_2=-1$

Work Step by Step

$e^x=e^{x^2-2}$ Using the One-to-One Property: $x^2-2=x$ $x^2-x-2=0~$ ($a=1,~b=-1,~c=-2$): $x=\frac{-(-1)±\sqrt {(-1)^2-4(1)(-2)}}{2(1)}=\frac{1±\sqrt 9}{2}=\frac{1±3}{2}$ $x_1=\frac{4}{2}=2$ and $x_2=\frac{-2}{2}=-1$
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