Logarithmic Graph with Geometric Construction

①This example demonstrates the construction of a logarithmic function graph along with associated geometric elements, using points, text labels, and function objects to illustrate connections between the log curve, perimeter, and centroid. ②Core mathematical concepts include logarithmic functions, curve sketching, subtraction, centroid (barycenter), and the interplay between algebra and geometry. ③Construction highlights: Based on the summary, the GeoGebra commands involve the Point command to create points, and objects such as functions a, f, g, text labels text1 through text4, and points A, B, C, D, M, which are used to annotate key positions on the log curve and display computed values, possibly for demonstrating transformations like shifts or scaling, or intersections with axes. ④This is suitable for high school or early college students learning properties of logarithmic functions, function graph transformations, and geometric-algebraic integration, and for teachers creating interactive materials to visualize monotonicity, asymptotes, and geometric features like centroids.