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: 103

Answer

$x =\dfrac{(\ln{8})-5}{2}$

Work Step by Step

Take the natural logarithm of both sides to obtain: $\ln{e^{2x+5}} = \ln{8}$ RECALL: $\ln{e^a} = a$ Use the rule above to obtain: $2x+5=\ln{8}$ Subtract by $5$ on both sides of the equation to obtain: $\begin{array}{ccc} &2x+5 -5 &= &\ln{8}-5 \\&2x &= &\ln{8}-5 \end{array}$ Divide by $2$ on both sides of the equation to obtain: $x =\dfrac{\ln{8}-5}{2}$
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