College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding: 102

Answer

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

Work Step by Step

Take the natural logarithm of both sides to obtain: $\ln{e^{-2x}} = \ln{(\frac{1}{3})}$ RECALL: $\ln{e^a} = a$ Use the rule above to obtain: $-2x=\ln{(\frac{1}{3})}$ Divide by $-2$ on both sides of the equation to obtain: $x =\dfrac{\ln{(\frac{1}{3})}}{-2} \\x =-\dfrac{\ln{(\frac{1}{3})}}{2}$
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