Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 36

Answer

$x=\frac{8}{9}$

Work Step by Step

We are given that $8^{3x-2}=4$. Both of these numbers are powers of 2, so we can rewrite the equation as $(2^{3})^{3x-2}=2^{9x-6}=2^{2}$. 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, $9x-6=2$. To solve for x, add 6 to both sides. $9x=8$ Divide both sides by 9. $x=\frac{8}{9}$
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