Answer
$t=0.554$
Work Step by Step
$4^{-3t}=0.10$
$\log_44^{-3t}=\log_40.10~~$ (Using the Inverse Property: $\log_aa^x=x$):
$-3t=\log_40.10$
$t=-\frac{1}{3}\log_40.10=-\frac{1}{3}\frac{\ln0.10}{\ln4}\approx0.554$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 26
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