College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.3 - Exponential Functions - 6.3 Assess Your Understanding - Page 436: 69


$x = \dfrac{3}{2}$

Work Step by Step

To solve the given equation, make the two sides have the same base. Note that $4=2^2$ so the given equation is equivalent to: $2^{2x-1}=2^2$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $2x-1 = 2$ Add 1 to both sides of the equation to obtain: $2x=2+1 \\2x=3$ Divide 2 to both sides of the equation to obtain: $x = \dfrac{3}{2}$
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