Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set: 34

Answer

$x=-\dfrac{7}{2}$

Work Step by Step

$4^{3x-7}=32^{2x}$ Rewrite $4$ as $2^{2}$ and $32$ as $2^{5}$: $(2^{2})^{3x-7}=(2^{5})^{2x}$ Multiply the exponents on both sides of the equation: $2^{6x-14}=2^{10x}$ If $2^{6x-14}=2^{10x}$, then $6x-14=10x$ $6x-14=10x$ Solve for $x$: $6x-10x=14$ $-4x=14$ $x=\dfrac{14}{-4}$ $x=-\dfrac{7}{2}$
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