Contextualization

Logarithm is a fundamental mathematical concept that has a series of applications in the real world, as well as in academic fields such as mathematics, engineering, and computer science. The main idea of logarithm is to transform multiplications into additions, making calculations more manageable.

The logarithm of a number is the exponent by which another fixed number - the base - must be raised to produce that number. Thus, it is an inverse operation of exponentiation. For example, the logarithm in base 10 of 1000 is 3, because 10 to the power of 3 equals 1000.

Logarithms have significant importance from a purely theoretical point of view, as they are keys to understanding many concepts in different fields of mathematics. For example, logarithms are used in solving differential equations, which are the basis for modeling and prediction in many fields, including physics, economics, and engineering.

Furthermore, the idea behind logarithms is applied practically in various everyday situations. For example, the Richter scale, used to measure the magnitude of earthquakes, and the pH scale, used to indicate the acidity or alkalinity of a solution, are both logarithmic measures. In both cases, small differences in measured values can represent large variations in reality, which is a feature of logarithms.

Practical Activity: Logarithm in Real Life

Project Objective

The objective of this activity is for students to apply the concept of logarithm in a real-world context. They should create an engaging presentation that demonstrates the relevant application of logarithm.

Detailed Project Description

In this project, students will first research a practical situation where logarithm is used. Then, they should develop a problem involving this situation and solve this problem using logarithms. Finally, they should produce a presentation, explaining the problem and its solution, as well as the theoretical foundation of logarithms.

Necessary Materials

• Books, websites, videos, and other resources for researching logarithm and its applications
• Paper and pen or digital tools for notes and calculations
• Computer with presentation software to create the final presentation

Step by Step

1. Research and Group Discussion: Students should research the various real-world applications of logarithm. Then, they should gather and discuss the information found, and choose a situation for the project.

2. Problem Development: Together, students should create a problem involving the chosen situation that requires logarithm to be solved.

3. Problem Solving: Applying their knowledge of logarithm, students should solve the created problem. It is important that they write down all the steps of the solution to be able to explain them in the presentation.

4. Presentation Creation: With the problem solved, students should prepare a presentation. The presentation should include the definition of logarithm, an explanation of how it is used in the chosen situation, the description and solution of the problem, and the conclusion about the importance of logarithm in practical situations.

5. Review and Improvement: Students should review the entire work and improve whatever is necessary.

Description of Deliverables and Connection with Activities

Students will deliver the presentation they created and a written report. The presentation should be organized and clear, and the report should follow the following topics:

1. Introduction: Students should explain the importance and application of logarithms in the real world and the project's objective.

2. Development: They should describe the chosen situation, the created problem, and the step-by-step solution, detailing the use and role of logarithm throughout the process.

3. Conclusion: Students should summarize the main points of the project, what they learned, and the conclusions they drew about the practical application of logarithms.

4. Bibliography: List of sources used in research and work development.

Completing the suggested activities above will result in the delivery of the presentation and the report. Both documents should be clear, complete, and demonstrate students' understanding of logarithm and its practical application.