Geometric “Anatomy” Construction for a Logarithmic Function

This example demonstrates, via geometric construction, how to dissect a logarithmic function’s key behavior by translating log relationships into proportional length changes inside a similarity-based configuration. The core ideas are logarithmic functions, graphing/visual interpretation, and using similar triangles (and related proportional reasoning) to connect algebraic log rules with measurable geometric quantities. Construction-wise, the GeoGebra commands highlighted by the construct summary are Point, Intersect, and Vector: points and intersection objects (e.g., the various named points such as g, h, A, B, C, D, E, F, G, H, I, J) define the framework, while Vector helps encode direction/scale relationships needed to represent the functional correspondence. Additional objects like eq1 and multiple labeled items (e.g., k, k_{1}, k1, and text annotations) are used to express constraints and display the derived relationships on the figure. Suitable for high school to early college lessons on functions, geometric construction, and using models to build intuition about logarithms and their graphical behavior.