Geometric Verification of Logarithm Properties

This GeoGebra example demonstrates well-known properties of logarithms through a geometric construction and interactive transformations. Instead of relying only on algebraic manipulation, it visualizes how logarithmic relationships can be represented via measurable geometric lengths and how they remain consistent under corresponding transformations. The key mathematical ideas include fundamental logarithm identities (relations among powers, products, quotients, and change of base) and the mapping between a logarithmic function and geometric metric data (segment/vector length). Construction highlights: Segment, Vector, and Length are used to build and measure the essential segments and vectors; Translate and RotateText support transformation-based visualization and clear labeling; Midpoint, Semicircle, and Point create auxiliary structures for enforcing the geometric equivalences; Textfield is employed to parameterize the scene and explore how the depicted relationships persist. Suitable for upper secondary and early university lessons, classroom demonstrations, and exploratory learning connecting functions with geometric construction.