Math Example: Laws of Logarithms: Example 10

Topic

Logarithms

Description

This example demonstrates the simplification of the logarithmic expression log₂(128) - log₂(4) using the quotient property of logarithms. The solution applies the rule log_n(a) - log_n(b) = log_n(a/b) to rewrite the expression as log₂(128/4), which simplifies to log₂(32). Since 32 = 2⁵, the final answer is 5.

Logarithms are a fundamental concept in advanced mathematics, particularly in algebra and calculus. These examples help teach logarithmic properties by providing step-by-step demonstrations of how to manipulate and simplify logarithmic expressions. By working through various scenarios, students can gain a deeper understanding of the rules governing logarithms and how to apply them in different contexts.

It's crucial for students to see multiple worked-out examples to fully grasp logarithmic concepts. Each example reinforces the principles while introducing slight variations, helping students recognize patterns and develop problem-solving strategies. This approach builds confidence and proficiency in handling logarithmic expressions, preparing students for more complex mathematical challenges.

Teacher's Script: Let's look at this example involving the difference of logarithms. We have log₂(128) - log₂(4). When we subtract logarithms with the same base, we can use the quotient rule. This means we can rewrite it as log₂(128/4). Now, what's 128 divided by 4? That's right, it's 32. So we have log₂(32). Remember, 32 is 2 to what power? It's 2⁵. Therefore, log₂(32) = 5. This example shows how we can use logarithm properties to simplify expressions and find exact values.

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