Indices and Logarithms - Mathematics (Senior Secondary)
This course provides a comprehensive guide to indices and their inverse, logarithms. It treats them not as separate topics, but as two sides of the same coin. The course begins with a mastery of the laws of indices before using that knowledge to define and derive the principles of logarithms, which are essential tools for simplifying complex calculations.
A command of indices and logarithms is non-negotiable for success in any advanced science, technology, engineering, or mathematics (STEM) field. These concepts are fundamental to modelling exponential growth and decay, analysing data on logarithmic scales (like pH or decibels), and solving advanced equations in calculus and physics.
By the end of this course, you will be able to confidently apply the laws of indices to simplify expressions and solve equations. You will understand the definition of a logarithm, read logarithm and antilogarithm tables, and use them to perform complex calculations involving multiplication, division, powers, and roots.
This course is built for students preparing for higher-level mathematics. It is also essential for anyone entering scientific or financial fields who needs a strong command of these foundational calculation tools. A solid understanding of basic algebra is required.
Enrolment valid for 12 months
Course Chapters
1. Introduction2
1. Introduction
2
This chapter introduces the core focus of the course. We will define indices and logarithms and immediately establish the fundamental inverse relationship between them.
By the end of this chapter, you will understand the course structure. You will be able to explain how logarithms are directly connected to indices, setting the stage for all future lessons.
Concept Overviews
2 Lessons
2. Working with Indices31
2. Working with Indices
3
1
This chapter is dedicated to achieving proficiency with indices. We will review standard form and then conduct a rigorous study of the laws of indices and their application.
By the end of this chapter, you will be able to recall and apply all the laws of indices. You will use them efficiently to simplify complex expressions and solve indicial equations.
Concept Overviews
3 Lessons
Problem Walkthroughs
1 Lesson
3. Understanding Logarithms31
3. Understanding Logarithms
3
1
This chapter uses your knowledge of indices to build a solid conceptual understanding of logarithms. We will formally define a logarithm and derive its laws directly from the laws of indices.
By the end of this chapter, you will be able to define a logarithm as the inverse of an index. You will understand the laws of logarithms and interpret logarithmic graphs.
Concept Overviews
3 Lessons
Problem Walkthroughs
1 Lesson
4. Using Logarithm Tables21
4. Using Logarithm Tables
2
1
This chapter focuses on the practical application of logarithms as a computational tool. You will learn the mechanical skills of reading logarithm and antilogarithm tables to solve complex arithmetic problems.
By the end of this chapter, you will be able to read logarithm and antilogarithm tables accurately. You will use these tables to perform calculations that would be tedious by hand.
Concept Overviews
2 Lessons
Problem Walkthroughs
1 Lesson
5. Conclusion and Next Steps2
5. Conclusion and Next Steps
2
This final chapter summarises the key skills covered in the course. It reinforces the connection between indices and logarithms and prepares you for more advanced topics.
By the end of this chapter, you will have reviewed the laws and applications of indices and logarithms. You will understand how these tools are used in higher-level mathematics.
Concept Overviews
2 Lessons