Answer
$\frac{ln{3}}{2}$.
Work Step by Step
If $e^{-2x}=\frac{1}{3}$, then by taking the natural logarithm of both sides we get $-2x=ln{\frac{1}{3}}$, therefore $x=\frac{ln{\frac{1}{3}}}{-2}=\frac{-ln{3}}{-2}=\frac{ln{3}}{2}$.
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 296: 102
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