Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 44

Answer

$\ln {x}+x$

Work Step by Step

Recall: (1) $\sqrt[m]{a}=a^{\frac{1}{m}}$ (2) $\log_a {x^n}=n\cdot \log_a {x}$. (3) $\log_a{xy}=\log_a{x} +\log_a{y}$ (4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$ (5) $\ln {e}=1$ (6) $\ln {e^x}=x$ Use Rule (3) above to obtain: $\ln {(x\cdot e^x)}=\ln {x}+ \ln {(e^x)}.$ Use Rule (6) above to obtain: $\ln {x}+ \ln {(e^x)}=\ln {x}+x$
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