Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - Chapter Review - Review Exercises - Page 113: 52

Answer

$x=\displaystyle \frac{1}{2}$

Work Step by Step

$(\displaystyle \frac{9}{16})^{x}=\frac{3}{4}\qquad \color{blue}{\text{ ...recognize } 9=3^{2}, 16=4^{2}}$ $[(\displaystyle \frac{3}{4})^{2}]^{x}=\frac{3}{4}\qquad \color{blue}{\text{ ...apply } (a^{n})^{m}=a^{nm},\quad a^{1}=a}$ $(\displaystyle \frac{3}{4})^{2x}=(\frac{3}{4})^{1}\qquad \color{blue}{\text{ ...equate the exponents } }$ $2x=1$ $x=\displaystyle \frac{1}{2}$
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