Math Example: Laws of Logarithms: Example 09

Topic

Logarithms

Description

This example focuses on simplifying the natural logarithm expression ln(5 * e²) using logarithmic properties. The solution applies the product rule of logarithms, log_n(a * b) = log_n(a) + log_n(b), to break down the expression into ln(5) + ln(e²). Since ln(e²) = 2, the final simplified form is ln(5) + 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 natural logarithm example. We have ln(5 * e²). Remember, when we have a product inside a logarithm, we can split it into a sum of logarithms. So, this becomes ln(5) + ln(e²). What's special about ln(e²)? That's right, it simplifies to just 2 because e is the base of natural logarithms. So our final answer is ln(5) + 2. This example shows how we can use the product rule of logarithms along with the special property of natural logarithms to simplify expressions.

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