Answer
$\ln{x}+x$
Work Step by Step
Recall:
$\log_a{(MN)} = \log_a{M}+\log_a{N}$
Using the rule above gives:
$\ln(x e^x) = \ln{x}+\ln{\left(e^x\right)}$
Recall also that $\ln{e^x} = x$
Thus,
$\ln{(x e^x)} = \boxed{\ln{x}+x}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 331: 44
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