Math Example: Laws of Logarithms: Example 11

Topic

Logarithms

Description

This example focuses on simplifying the logarithmic expression log(300) - log(3) using the quotient property of logarithms. The solution applies the rule log(a) - log(b) = log(a/b) to rewrite the expression as log(300/3), which simplifies to log(100). Since 100 = 10², the final answer is 2.

Logarithms are a crucial topic in mathematics, particularly in algebra and calculus. These examples help students understand the properties of logarithms and how to manipulate logarithmic expressions. By working through various scenarios, students learn to apply logarithmic rules effectively and gain confidence in solving more complex problems involving logarithms.

Providing multiple worked-out examples is essential for students to fully grasp logarithmic concepts. Each example reinforces the basic principles while introducing slight variations, helping students recognize patterns and develop problem-solving strategies. This approach allows students to see how logarithmic properties can be applied in different contexts, enhancing their understanding and ability to tackle diverse logarithmic problems.

Teacher's Script: Now, let's look at this example with common logarithms. We have log(300) - log(3). When we subtract logarithms with the same base, we can use the quotient rule. This means we can rewrite it as log(300/3). What's 300 divided by 3? That's right, it's 100. So we have log(100). Now, 100 is 10 squared, right? Therefore, log(100) = log(10²) = 2. This example shows how we can use logarithm properties to simplify expressions and find exact values, even when working with common logarithms.

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