Math Example: Laws of Logarithms: Example 04

Topic

Logarithms

Description

This example illustrates the simplification of log₂(4/x) + log₂(9x) using logarithm properties. The solution applies the property that the sum of logarithms with the same base equals the logarithm of the product of their arguments. Here, log₂(4/x) + log₂(9x) simplifies to log₂(36), which further simplifies to log₂(2⁶), resulting in 6.

Understanding the Laws of Logarithms is crucial for manipulating and simplifying logarithmic expressions, especially those involving variables. These examples provide students with practical applications of these laws, helping them develop problem-solving skills and mathematical intuition. By working through various scenarios, students learn to recognize patterns and apply appropriate strategies, even when dealing with expressions containing variables.

Exposure to multiple worked-out examples is essential for students to fully comprehend logarithmic concepts. Each example presents a unique situation, allowing students to see how the laws of logarithms can be applied in different contexts, including those with variables. This repetition reinforces understanding and builds confidence in tackling complex problems.

Teacher's Script: As we examine this example, notice how the variable x cancels out when we multiply the arguments. This is a key insight when working with logarithmic expressions containing variables. Can you think of other situations where this cancellation might occur?

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