Math Example: Laws of Logarithms: Example 13

Topic

Logarithms

Description

This example focuses on simplifying the logarithmic expression log₂(4x²) - log₂(2x) 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(4x²/2x). This simplifies to log₂(2x), which can be further expanded using the product rule of logarithms to log₂(2) + log₂(x), resulting in 1 + log₂(x).

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 involving variables. By working through various scenarios, students learn to apply logarithmic rules effectively and gain confidence in solving more complex problems involving logarithms and algebraic expressions.

Providing multiple worked-out examples is essential for students to fully grasp logarithmic concepts, especially when variables are involved. 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 in algebra and other mathematical fields.

Teacher's Script: Now, let's look at this example with logarithms and variables. We have log₂(4x²) - log₂(2x). When we subtract logarithms with the same base, we can use the quotient rule. This means we can rewrite it as log₂(4x²/2x). Let's simplify the fraction inside: 4x² divided by 2x is 2x. So we have log₂(2x). Can we simplify this further? Yes, we can use the product rule of logarithms to split this into log₂(2) + log₂(x). What's log₂(2)? It's 1. So our final answer is 1 + log₂(x). This example shows how we can use multiple logarithm properties to simplify expressions involving variables.

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