Answer
$f^{-1}(x) = \log_5 x$
Work Step by Step
$f(x) = 5^{x}$
Let $f(x) = y$
$y = 5^{x}$
Swap the variables $x$ and $y$, then solve for $y$ to find the inverse:
$x = 5^{y}$
$y = \log_5 x$
$f^{-1}(x) = \log_5 x$
Intermediate Algebra: Connecting Concepts through Application
by Clark, Mark; Anfinson, Cynthia
Published by
Brooks Cole
ISBN 10:
0-53449-636-9
ISBN 13:
978-0-53449-636-4
Chapter 6 - Logarithmic Functions - Chapter Test - Page 543: 17
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