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: 104

Answer

$x =-\dfrac{(\ln{13})-1}{2}$

Work Step by Step

Take the natural logarithm of both sides to obtain: $\ln{e^{-2x+1}} = \ln{13}$ RECALL: $\ln{e^a} = a$ Use the rule above to obtain: $-2x+1=\ln{13}$ Subtract by $1$ on both sides of the equation to obtain: $\begin{array}{ccc} &-2x+1 -1 &= &\ln{13}-1 \\&-2x &= &\ln{13}-1 \end{array}$ Divide by $-2$ on both sides of the equation to obtain: $x =\dfrac{\ln{13}-1}{-2} \\x =-\dfrac{\ln{13}-1}{2}$
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