Algebra 2 Common Core

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

Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 50

Answer

$x=3e^4$

Work Step by Step

Recall: $\ln{a}-\ln{b} = \ln{\left(\frac{a}{b}\right)}$ Thus, using the rule above gives: \begin{align*} \ln{\left(\frac{x}{3}\right)}&=4 \end{align*} Recall: $\ln{x}=a \longleftrightarrow e^a=x$ Hence, \begin{align*} \ln{\left(\frac{x}{3}\right)}=4 &\longrightarrow \frac{x}{3}=e^4\\\\ &x=3 \cdot e^4 \end{align*} Check: \begin{align*} \ln{(3\cdot e^4)}- \ln{3}&=4\\\\ \ln{\left(\frac{3e^4}{3}\right)}&=4\\\\ \ln{e^4}&=4\\\\ 4&=4 \end{align*}
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