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: 35

Answer

$x=0$

Work Step by Step

Subtract $5$ from each side to obtain: $$e^{3x}=1$$ RECALL: $$\ln{x}=y \longleftrightarrow e^y=x$$ Use the definition above to obtain: \begin{align*} \ln{1}&=3x\\\\ \frac{\ln{1}}{3}&=\frac{3x}{3}\\\\ \frac{\ln{1}}{3}&=x \end{align*} Use a scientific calculator to obtain: $$x=0$$
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