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: 24

Answer

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

Work Step by Step

$64^{x}=16$ Since $64=4^{3}$ and $16=4^{2}$, rewrite the equation as $(4^{3})^{x}=4^{2}$: $(4^{3})^{x}=4^{2}$ Rewrite this equation again, as $4^{3x}=4^{2}$: $4^{3x}=4^{2}$ If $4^{3x}=4^{2}$, then $3x=2$: $3x=2$ Solve for $x$ by taking the $3$ to divide the right side: $x=\dfrac{2}{3}$
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