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: 47



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) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$ Use Rule (3) above to obtain: $\ln{(x^2\cdot \sqrt{1-x})}\\ =\ln {(x^2)}+\ln{\sqrt{1-x}}\\ =\ln {(x^2)}+\ln{(1-x)^{\frac{1}{2}}}$. Use Rule (2) above to obtain: $\ln {(x^2)}+\ln{(1-x)^{\frac{1}{2}}}\\ =2\ln{(x)}+\frac{1}{2}\ln{(1-x)}$
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