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: 67

Answer

$x=\frac{1}{2}$

Work Step by Step

We rewrite both sides, so that the base is $e$ on both sides. $e^{4x-1}=(e^2)^x$ By the law of exponents: $(a^x)^y=a^{xy}$ $(e^2)^x=e^{2x}$ Thus, $e^{4x-1} = e^{2x}$ Both sides have the same base, so set the exponents equal to have: $4x-1=2x$ $4x=2x+1$ $4x-2x=1$ $2x=1$ $x=\frac{1}{2}$
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