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 306: 108


Since $\log_a {x^n}=n\cdot \log_a {x}$, then $f(x^{\alpha})=\log_a{(x^{\alpha})}=\alpha \cdot \log_a{x}=\alpha \cdot f(x)$

Work Step by Step

We know that $\log_a {x^n}=n\cdot \log_a {x}$. Hence, $f(x^{\alpha})=\log_a{x^{\alpha}}=\alpha \cdot \log_a{x}=\alpha \cdot f(x)$
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