Answer
$g^{-1}(t) = \log_2 t$
Work Step by Step
$g(t) = 2^{t}$
Let $g(t) = y$
$y = 2^{t}$
Swap the $t$ and $y$ variables then solve for $y$ to find the inverse:
$t = 2^{y}$
$y = \log_2 t$
$g^{-1}(t) = \log_2 t.$
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 - 6.2 Logarithmic Functions - 6.2 Exercises - Page 504: 86
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