## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

# Chapter 4 - Exponential and Logarithmic Functions - Section 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 331: 43

#### Answer

$\ln{x}-x$

#### Work Step by Step

Recall: $\log_a{\left(\dfrac{M}{N}\right)} = \log_a M-\log_a N$ Using the rule above gives: $\ln \left(\dfrac{x}{e^x} \right) = \ln{x}-\ln{\left(e^x\right)}$ Recall also that $\ln e^x = x$. Thus, $\ln{\left(\dfrac{x}{e^x} \right)} = \boxed{\ln{x}-x}$

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