Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises - Page 457: 64

Answer

$y=\frac{1}{2} \cdot 2^x$

Work Step by Step

To find the inverse of the given function, perform the following steps: (1) Interchange $x$ and $y$: $$x=\log_2{2y}$$ (2) Write the equation in exponential form using the definition $y=\log_a{x} \longleftrightarrow a^y=x$: $$2^x=2y$$ (3) Solve for $y$: \begin{align*} 2^x&=2y\\\\ \frac{2^x}{2}&=y\\\\ y&=\frac{1}{2} \cdot 2^x \end{align*}
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