Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 75

Answer

$x=\dfrac{1}{64}$

Work Step by Step

RECALL: $\log_b{a}=y \longrightarrow b^y=a$ With $a=x$, $b=4$, and $y=-3$, use the rule above to the given expression to obtain: $4^{-3}=x$ Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain: $\dfrac{1}{4^3} = x \\\dfrac{1}{4(4)(4)}=x \\\dfrac{1}{16(4)}=x \\\dfrac{1}{64}=x$
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