Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-6 Natural Logarithms - Practice and Problem-Solving Exercises - Page 481: 36

Answer

$x\approx 23.752$

Work Step by Step

Add $8$ to each side to obtain: $$e^{\frac{x}{9}}=14$$ RECALL: $$\ln{x}=y \longleftrightarrow e^y=x$$ Use the definition above to obtain: \begin{align*} \ln{14}&=\frac{x}{9}\\\\ 9(\ln{14})&=9\left(\frac{x}{9}\right)\\\\ 9\ln{14}&=x \end{align*} Use a scientific calculator to obtain: $$x\approx 23.752$$
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