Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.5 Logarithmic Functions - 2.5 Exercises - Page 99: 74

Answer

$\log_aX^r=\log_a(X.X.X...X)$ with $X.X.X...X$ equals to $X^r$ We have the property $\log_axy=\log_ax+\log_ay$ so $\log_a(X.X.X...X)=\log_aX+\log_aX+...+\log_aX$ with $\log_aX+\log_aX+...+\log_aX$ is $r$ times of $\log_aX$ $\rightarrow \log_aX+\log_aX+...+\log_aX=r\log_aX$ Hence, $\log_aX^r=r\log_aX$

Work Step by Step

As given above
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