# Logarithmic function. Properties.

- Author:
- cracana dumitru, Judith Hohenwarter

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

- Subject:
**Mathematics** - Grade Level:
**10**th grade - Duration: about
*50 min* - 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 :- 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.

*Computer and projector**for teacher;**computers/ tablets for students.*

## Technology Integration

and . - In order to have no problems, before the lesson I will ensure that all pupils have their applets downloaded on their equipment.