Algebra: A Combined Approach (4th Edition)

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

Chapter 12 - Section 12.6 - Integrated Review - Functions and Properties of Logarithms: 22

Answer

$x=-8$

Work Step by Step

$4^{x-1}=8^{x+2}$ Rewrite $4$ as $2^{2}$ and $8$ as $2^{3}$: $(2^{2})^{x-1}=(2^{3})^{x+2}$ Multiply the exponents on both sides of the equation: $2^{2x-2}=2^{3x+6}$ If $2^{2x-2}=2^{3x+6}$, then $2x-2=3x+6$: $2x-2=3x+6$ Solve for $x$: $2x-3x=6+2$ $-x=8$ $x=-8$
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