Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises: 63

Answer

$f^{-1}(x) = \log_3 (\frac{x}{5})$

Work Step by Step

$f(x) = 5(3)^{x}$ Let $f(x) = y$ $y = 5(3)^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = 5(3)^{y}$ $\frac{x}{5} = (3)^{y}$ $y = \log_3 (\frac{x}{5})$ $f^{-1}(x) = \log_3 (\frac{x}{5})$
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