Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 46


$x=-\dfrac{\ln{1.5}}{\ln{2}}\approx -0.585$

Work Step by Step

Take the $\log_2$ of both sides: $\log_2{2^{-x}}=\log_2{1.5}\\-x=\log_2{1.5}$ Multiply $-1$ to both sides to obtain: $x=-\log_2{1.5}.$ We know that $\log_a {b}=\dfrac{\log_c {b}}{\log_c {a}}$ (Change of Base Formula). Hence, using the change-of-base formula and a calculator gives $x=-\log_2{1.5}=-\dfrac{\ln{1.5}}{\ln{2}}\approx-0.585$
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