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

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: 47


$2 \ln x+\frac{1}{2} \ln (1-x)$

Work Step by Step

Given: $\quad \quad \ln \left(x^{2} \sqrt{1-x}\right)$ Use the rule $\ln A B=\ln A+\ln B$ to obtain: \begin{align*} \ln\left(x^{2} \sqrt{1-x}\right)&=\ln x^{2}+\ln \sqrt{1-x}\\ &=\ln x^{2}+\ln (1-x)^{1 / 2} \end{align*} Using the rule $\quad\ln a^{m}=m \ln a$ gives: $$\ln\left(x^{2} \sqrt{1-x}\right)=2 \ln x+\frac{1}{2} \ln (1-x)$$
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