Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define logarithms and their relationship to exponents.
• Apply the properties of logarithms to solve real-life problems like calculating pH values.
• Use logarithms to solve for unknown variables in algebraic equations.

Lesson summary

This lesson explores the powerful connection between indices (powers) and logarithms. While indices help us understand rapid growth (like how money multiplies in a savings account or how a population grows), logarithms provide the tool to answer the question, "How long will it take?" We will discover that logarithms are not just abstract mathematical ideas; they are essential for solving real-world problems in finance, science (like chemistry and environmental science), and even technology. This lesson will equip you with the skills to apply logarithms to practical situations you might encounter in Ghana and beyond.

Lesson notes

Part 1: The Bridge from Indices to Logarithms

Let's start with what we already know: Indices.

An index (or power) tells us how many times to multiply a number by itself. For example, `10³ = 10 × 10 × 10 = 1000`. In this expression, 10 is the base, and 3 is the index or exponent.

Now, let's ask a different question: "To what power must we raise the base 10 to get the number 1000?" The answer, as we see above, is 3.

Evaluation guide

• Use mathematical connections to explore the relevance of surds, indices and logarithms
• and their applications to scientific concepts.
• In collaborative groups:
• ȉ Assign tasks to help learners apply the understanding of common logarithms to solve real -life