Answer
See graph and explanations.
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.
