Distances on a Logarithmic Scale

① This activity displays a logarithmic scale and lets the user define a number to visualize its position on the scale, then visualize the quotient of two numbers as a geometric distance. ② Core mathematical concepts include logarithms, logarithmic scaling, the relationship between ratios and distances, and the inverse nature of exponential and logarithmic functions. ③ Construction details: The GeoGebra commands Sequence and Segment are used to generate tick marks and connecting segments; objects include power1, power2 (power functions), number1, number2 (user inputs), g (logarithmic function graph), A, B (points), l1, l2 (scale lines), f (auxiliary function), and quotient (the ratio value). ④ Suitable for high school or introductory college students learning logarithms and exponents, also useful in statistics or data analysis to understand how multiplicative relationships become additive distances on a log scale.