Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define logarithms and explain their relationship with indices.
• State and apply the laws of logarithms to solve equations.
• Change the base of a logarithm to solve problems.
• Recognize how logarithms are used in real-world scenarios.

Lesson summary

This lesson builds upon your prior knowledge of indices to introduce the powerful concept of logarithms. Logarithms are essentially the "opposite" of exponents and provide a tool for solving equations where the unknown is a power. They are incredibly useful for handling numbers that are very large or very small. In Ghana, logarithms have applications in fields like finance (calculating investment growth over time), science (measuring earthquake intensity or the acidity of soil for farming), and engineering. By mastering logarithms, we gain a new and efficient way to model and solve complex real-world problems.

Lesson notes

Part 1: The Bridge Between Indices and Logarithms

The core idea of a logarithm is to answer the question: "What power do I need to raise a specific base to, in order to get a certain number?"

Definition: If bˣ = y, then we can write this statement in logarithmic form as logₑ(y) = x. b is the base. x is the exponent (or the logarithm). y is the number (or the argument).

We read logₑ(y) = x as "log to the base b of y is equal to x".

Evaluation guide

• Use the properties of logarithms and indices to solve equations involving logarithms,
• including changing the base.
• Collaborative Learning, Experiential Learning, Problem -based Learning, Project -based
• Learning and Talk for Learning