Lesson Notes By Weeks and Term v4 - SHS 1
NUMBER AND ALGEBRAIC PATTERNS
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NUMBER AND ALGEBRAIC PATTERNS
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 8
Grade code: 1.1.1.LI.6
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.1
Indicator code: 1.1.1.LI.6
Theme: MODELLING WITH ALGEBRA
Subtheme: NUMBER AND ALGEBRAIC PATTERNS
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This lesson introduces the concept of logarithms as the inverse of exponentiation (indices). We often encounter situations in real life where we need to find an unknown power or exponent. For example, how long will it take for an investment made through a mobile money platform to double? How long does it take for a population to reach a certain number? Logarithms provide us with the mathematical tool to answer these questions precisely. By understanding the relationship between indices and logarithms, we can solve complex problems in finance, science, and engineering that involve exponential growth and decay.
Part 1: The Relationship Between Indices and Logarithms
The core idea of a logarithm is to answer the question: "What exponent do I need to raise a certain base to, in order to get another number?"
Let's start with what we already know: Indices. We know that `2³ = 8`. In this expression: `2` is the base. `3` is the index or exponent. `8` is the result or number.
A logarithm rephrases this same relationship. The logarithm is the exponent. So, we can say: "The logarithm of 8 to the base 2 is 3". We write this as: `log₂(8) = 3`.