Math Example: Laws of Logarithms: Example 07

Topic

Logarithms

Description

This example demonstrates the simplification of a logarithmic expression with base 2 using the product property. The problem involves simplifying log₂(2 * 30). By applying the property that log_n(a * b) = log_n(a) + log_n(b), we can separate the logarithm of the product into the sum of logarithms. This results in log₂(2) + log₂(30), which simplifies to 1 + log₂(30). Further simplification leads to 1 + log₂(2 * 15), which becomes 2 + log₂(15).

The Laws of Logarithms are fundamental in simplifying complex logarithmic expressions. These examples help students understand how to apply these laws in various scenarios, including those with different bases. By working through different problems, students can recognize patterns and develop strategies for tackling similar questions in the future.

Exposure to multiple worked-out examples is crucial for students to fully grasp logarithmic concepts. Each example presents a unique scenario, allowing students to see how the laws of logarithms can be applied in different contexts. This repetition reinforces understanding and builds confidence in problem-solving skills, especially when dealing with expressions that require multiple steps of simplification.

Teacher's Script: Let's analyze this example step by step. Notice how we can simplify log₂(2) immediately to 1. This is a key property of logarithms that you should remember. Can you think of other bases where a similar immediate simplification would occur?

For a complete collection of math examples related to Logarithms click on this link: Math Examples: Laws of Logarithms Collection.