# Logarithmic function. Properties.

## This book contains the lesson project that introduces the logarithmic function and discovers the properties of this function.

• Subject: Mathematics
• Technology setting: Computer and projector for teacher, computers/ tablets for students.

## Topic.

Logarithmic function. Properties. The geometric representation of the graph of the logarithmic base function supraunitary and subunitary, identification of its inversion by right symmetry y = x (first bisector), solving some equations.

## Learning Outcomes

During the lesson, students:
• will discover the graph of the logarithmic function with a supraunit and subunit base;
• will see, through graphical reading, the properties of the functions: monotony, convexity, infinite variation (slope) ...
• will explore the sign of the logarithmic function;
• will identify the exponential function as the inverse logarithmic function.
After the lesson,students will know :
• the properties of the logarithmic function in relation to the base;
• students will know how to compare the logarithm of the same number in relation to the base;
• that the logarithmic function is inverse to the exponential function.
As a result of the lesson,students will be able to do it :
• to plot the logarithmic function graph;
• to compare two logarithms;
• to resolve some of the equations graphically.

## Lesson Objectives and Assessment

Lesson objectives:
• students can draw through points the graph of the logarithmic function;
• students can explain the properties of the logarithmic function;
• in relation to the base, can distinguish the differences between properties;
• identifies the inverse logarithmic function;
• can explain inequalities between logarithms;
• can read from the graph the sign of the logarithmic function.
Assessment:
• check the students' written notes;
• in applet 2, changing the logarithm base, students are required to observe the properties and list them;
• discussions about the power of infinite convergence of the logarithm with the help of the tangent slope to the graph.
Prior Knowledge:
• students need to be familiar with identifying the properties of a graphical reading function;
• students need to know the graph of the exponential function;
• students need to know the relationship between the function graphs and .

## Teaching Strategies

Methods and strategies:
• learning by discovery;
• questioning;
• conversation, observation.
Equipment:
• Computer and projector for teacher;
• computers/ tablets for students.

## Technology Integration

• Students need to be familiar with identifying the properties of a graphical reading function; to know the graph of the exponential function; to know the relationship between the function graphs and .
• In order to have no problems, before the lesson I will ensure that all pupils have their applets downloaded on their equipment.