Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.3 Logarithmic Functions - 4.3 Exercises - Page 447: 110

Answer

See explanations.

Work Step by Step

Step 1. Let $p=log_ax$, we have $x=a^p$ Step 2. We have $x^r=(a^p)^r=a^{pr}$, thus $pr=log_a(x^r)$ Step 3. Combine the above, we have $(log_ax)r=log_a(x^r)$ or $log_a(x^r)=r\ log_ax$
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