Lesson Notes By Weeks and Term v4 - SHS 2
REAL NUMBER AND NUMERATION SYSTEM
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REAL NUMBER AND NUMERATION SYSTEM
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Subject: Mathematics
Class: SHS 2
Term: 1st Term
Week: 3
Grade code: 2.1.1.LI.3
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.12
Indicator code: 2.1.1.LI.3
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: REAL NUMBER AND NUMERATION SYSTEM
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This lesson explores the powerful relationship between exponents (indices) and logarithms. We often encounter situations involving very large numbers (like the distance to stars) or very rapid growth (like mobile money adoption in Ghana or the spread of information). Logarithms are a mathematical tool that helps us manage and understand these large-scale numbers and rapid changes more easily. They essentially "tame" exponents, making complex calculations simpler. We will see how the rules you already know for indices are directly mirrored in the laws of logarithms, and we will apply these to solve practical problems we might face in finance, science, and more.
Part A: Quick Refresher on the Laws of Indices (Exponents)
Before we introduce logarithms, let's remember the laws of indices that you learned in JHS and SHS1. These are the foundation for everything we will do today. For any real numbers `a`, `m`, and `n` (where `a ≠ 0`): Product Law: `aᵐ × aⁿ = aᵐ⁺ⁿ` *Example:* `2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128` Quotient Law: `aᵐ ÷ aⁿ = aᵐ⁻ⁿ` *Example:* `5⁶ ÷ 5⁴ = 5⁶⁻⁴ = 5² = 25` Power Law: `(aᵐ)ⁿ = aᵐⁿ` *Example:* `(3²)³ = 3²ˣ³ = 3⁶ = 729` Zero Exponent: `a⁰ = 1` *Example:* `(500)⁰ = 1` Negative Exponent: `a⁻ⁿ = 1 / aⁿ` *Example:* `4⁻² = 1 / 4² = 1 / 16`
These rules are our essential tools. Now, let's build the bridge to logarithms. Part B: What is a Logarithm? The Inverse of an Exponent
A logarithm answers the question: "What exponent do I need to raise a specific base to, in order to get a certain number?"