Visualizing the Logarithm Change-of-Base Formula: log_b(x)=ln(x)/ln(b)

① This applet dynamically illustrates the change-of-base formula for logarithms, log_b(x)=ln(x)/ln(b), by showing how any logarithm can be expressed as a ratio of natural logarithms. ② The core mathematical concepts include logarithmic functions, the change-of-base identity, natural logarithms, and the behavior of function graphs. ③ Construction highlights: using GeoGebra's Point command to create key points, defining multiple function objects (f, g, h) and text objects (text1 through text18), and employing sliders (base, fak10, fak2) to adjust the base and scaling factors, thereby updating the graph and numerical values in real time to demonstrate the relationship between logarithms of different bases and the natural logarithm. ④ Suitable for high school and college students, this applet helps in understanding and verifying the change-of-base formula, and serves as an interactive tool for classroom demonstrations or self-directed exploration.