Answer
See below.
Work Step by Step
Given $f(x)=log_a(x)$, we have $\frac{f(x+h)-f(x)}{h}=\frac{log_a(x+h)-log_a(x)}{h}=\frac{log_a(\frac{x+h}{x})}{h}=\frac{log_a(1+\frac{h}{x})}{h}=log_a(1+\frac{h}{x})^{1/h}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
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 332: 104
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