Page 1: Introduction to Logarithmic Functions

This page introduces the concept of the logarithmic function and provides a graphical representation of specific examples.

Definition: A logarithmic function with base a (where a is positive and not equal to 1) is defined as y = log_a$x$, where x > 0.

The page includes two graphs:

1. Wykres funkcji logarytmicznej (Graph of the logarithmic function) y = log_1/2$$x
2. Graph of the function y = log_2$x$

Highlight: The graphs visually demonstrate the key properties of logarithmic functions, including their domain, range, and behavior for different x values.

The page also begins to list some properties of logarithmic functions, which are further elaborated on the next page.

Example: The graph of y = log_1/2$$x is shown to be a decreasing function, while y = log_2$x$ is an increasing function, illustrating how the base affects the function's behavior.

Overall Summary

The document provides a comprehensive overview of the logarithmic function, focusing on its definition, properties, and graphical representation. It covers the following key aspects:

• Definition of the logarithmic function with base a (a > 0, a ≠ 1)
• Graphical representation of logarithmic functions with different bases
• Detailed analysis of the properties of logarithmic functions
• Comparison between logarithmic functions with base 2 and base a > 1