Create an interactive application in Russian that visualizes standard logarithms using other equations. Users should be able to select from a set of predefined logarithmic functions, such as log(x), log(2x), log(x^2), and see them plotted on a Cartesian coordinate system.

User Interface
- Implement a dropdown menu or buttons to allow users to select different logarithmic equations for visualization.
- Ensure the interface is intuitive and user-friendly, with clear labeling and easy navigation.

Visualization Features
- Plot the selected logarithmic function on a Cartesian plane, illustrating its behavior.
- Decompose each logarithm into its constituent mathematical functions for clearer understanding.
- Provide interactive elements that allow users to manipulate variables and see real-time updates on the plots.

Best Practices
- Use clear, distinguishable colors for different plots to enhance readability.
- Allow users to zoom in and out of the graph for more detailed examination of the functions.
- Provide a legend or key to explain the visual representation of each function.

Additional Considerations
- Include explanatory tooltips or a help section to assist users in understanding how to interpret the visualizations.
- Consider performance optimization for smooth real-time updates as users interact with the application.

Визуализация  расчета стандартных логарифмов через другие уравнения
возьми несколько логарифмов чтобы можно было каждый из них выбрать и увидеть как на декартовой системе координат из каких функций он состоит.

Q: Какие конкретно логарифмы вы хотите визуализировать?
A: Например, log(x), log(2x), log(x^2)

Q: Какой интерфейс вы хотите использовать для выбора логарифмов?
A: Выпадающий список или кнопки?