Geometric Representation of a Logarithm

This is a geometric representation of what a logarithm does. For the two equations - y is the total distance of the line segment, which can be adjusted by moving point B - b is the base, the proportion or constant - x=b-1 which is the number of times b is multiplied or divided
Consider the following questions: Do the points change when the distance is adjusted? What happens to the points as b, the base, increases? As b decreases? Move the slider to b=1. What happens to the points? Why? What is the algebraic equivalent of this operation? Move the slider to b=0. What happens to the points? Why? Compare the x-coordinates of the points when b=2 and b=10. How would you describe the sequence of numbers?