Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.3 - Exponential Functions - Exercise Set: 36

Answer

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

Work Step by Step

We are given that $4^{3x-7}=32^{2x}$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{2})^{3x-7}=(2^{5})^{2x}$. Therefore, $2^{6x-14}=2^{10x}$ From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$). Therefore, $6x-14=10x$. Subtract 6x from both sides. $4x=-14$ Divide both sides by 4. $x=-\frac{14}{4}=-\frac{7}{2}$
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