Comparing Graphs of log(x) and log(1/x)

① This GeoGebra example dynamically illustrates the graphs of the logarithmic functions log(x) and log(1/x), highlighting their symmetry about the x-axis and the effect of changing the base. ② Core mathematical concepts include logarithmic properties (especially log(1/x) = -log(x)), graph transformations, base variation (common vs natural log), and piecewise function construction. ③ Construction details: The example uses the If command to build piecewise functions, Point objects for draggable points, a button (button1) and sliders to adjust parameters dynamically. Objects include functions f, g, h, multiple text objects (text1–text11) for displaying expressions and values, a list (list1) for key points, and variables base01 and ba to control the base, allowing flexible exploration of logarithmic graphs under different bases. ④ Suitable for high school and above students learning logarithmic properties, and for teachers demonstrating function transformations and symmetry in class, reinforcing understanding of logarithmic rules and graphical behavior.