Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1: 26

Answer

$x=-\frac{1}{2}\ln(\frac{5}{3})$

Work Step by Step

Divide each side by $3$ to get $e^{-2x}=\frac{5}{3}$. Take the natural logarithm of each side to get $ln(e^{-2x})=ln(\frac{5}{3})$, or $-2x=ln(\frac{5}{3})$. Dividing each side by $-2$ gives $x=-\frac{1}{2}\ln(\frac{5}{3})$.
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