Math Example: Laws of Logarithms: Example 17

Topic

Logarithms

Description

This example focuses on simplifying the logarithmic expression log(√(10) / 10) using the quotient property of logarithms. The solution applies the rule log(a/b) = log(a) - log(b) to rewrite the expression as log(√(10)) - log(10). This simplifies to log(10^(1/2)) - log(10), which further reduces to 1/2 - 1, resulting in -1/2.

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 involving square roots and fractions. 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 dealing with square roots and fractional exponents. 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: Let's examine this example involving a logarithm with a square root. We have log(sqrt(10) / 10). First, we can use the quotient rule of logarithms to split this into log(√(10)) - log(10). Now, let's focus on log(√(10)). Remember, √(10) is the same as 10^(1/2). So, this becomes log(10^(1/2)). Using the power rule of logarithms, this simplifies to (1/2)log(10). What's log(10)? It's 1. So we have 1/2 - 1. Our final answer is -1/2. This example demonstrates how we can use multiple logarithm properties to simplify expressions involving square roots and fractions.

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