## Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley

# Chapter 5 - Logarithmic Functions - Exercises to Skills for Chapter 5 - Page 232: 43

#### Answer

$x \approx 0.439$

#### Work Step by Step

Take the natural log of both sides to get $$\ln e^{-5x} = \ln 9$$ Since $\ln a^b=b \ln a$, the equation becomes $$-5x \ln e = -5x = \ln 9$$ Divide both sides by $-5$ to get $$x=\frac{\ln 9}{-5} \approx-0.439$$

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