Math Example: Laws of Logarithms: Example 01

Topic

Logarithms

Description

This example demonstrates the simplification of log base 2 of 4 plus log base 2 of 8 using logarithm properties. The solution utilizes the property that the sum of logarithms with the same base equals the logarithm of the product of their arguments. In this case, log₂(4) + log₂(8) simplifies to log₂(32), which further simplifies to log₂(2⁵), resulting in 5.

The Laws of Logarithms are fundamental in simplifying complex logarithmic expressions. These examples help students understand how to apply these laws in various scenarios, making calculations more manageable and efficient. 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.

Teacher's Script: Let's examine this example closely. Notice how we combine the logarithms with the same base by multiplying their arguments. This is a key property of logarithms that we'll use often. Can you think of other situations where this property might be useful?

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