College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 68

Answer

$x=\frac{-3}{2}$

Work Step by Step

We rewrite both sides, so that the base is $e$ on both sides. $e^{3-x}=(e^3)^{-x}$ By the law of exponents: $(a^x)^y=a^{xy}$ $(e^3)^{-x}=e^{-3x}$ The rewritten equation: $e^{3-x}=e^{-3x}$ Then, since the base of both sides are the same, we set the exponents equal, because the two sides are equal only if the powers are equal too: $3-x=-3x$ $2x=-3$ $x=\frac{-3}{2}$
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