Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set - Page 476: 115

Answer

See graph and explanations.
1582937372

Work Step by Step

Step 1. Graph the function $y=log_3(x)=\frac{log(x)}{log3}$ as shown with the red curve in the figure. Step 2. Graph the function $y=log_{25}(x)=\frac{log(x)}{log(25)}$ as shown with the blue curve in the figure. Step 3. Graph the function $y=log_{100}(x)=\frac{log(x)}{log(100)}$ as shown with the green curve in the figure. a. It can be seen that in the interval of $(0,1)$, the green curve $y=log_{100}(x)=\frac{log(x)}{log(100)}$ is on the top, while the red curve $y=log_3(x)=\frac{log(x)}{log3}$ is on the bottom. b. It can be seen that in the interval of $(1,\infty)$, the red curve $y=log_3(x)=\frac{log(x)}{log3}$ is on the top, while the green curve $y=log_{100}(x)=\frac{log(x)}{log(100)}$ is on the bottom. c. For $y=log_b(x), b\gt1$, in the interval of $(0,1)$, the curve with the biggest $b$ value will be on top, while in the interval of $(1,\infty)$, the curve with the smallest $b$ value will be on top.
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