Math Example: Laws of Logarithms: Example 03

Topic

Logarithms

Description

This example demonstrates the simplification of natural logarithm of (2/e) plus natural logarithm of (1/2e) using logarithm properties. The solution applies the property that the sum of logarithms equals the logarithm of the product of their arguments. In this case, ln(2/e) + ln(1/2e) simplifies to ln(1/e²), which further simplifies to ln(e^-2), resulting in -2.

The Laws of Logarithms are crucial in manipulating and simplifying complex logarithmic expressions. These examples help students understand how to apply these laws in various scenarios, particularly when dealing with natural logarithms and the constant e. By working through different problems, students can recognize patterns and develop strategies for tackling similar questions in the future.

Exposure to multiple worked-out examples is essential for students to fully grasp logarithmic concepts. Each example presents a unique scenario, allowing students to see how the laws of logarithms can be applied in different contexts. This repetition reinforces understanding and builds confidence in problem-solving skills, especially when dealing with more complex expressions involving e.

Teacher's Script: Let's analyze this example carefully. Notice how we combine the natural logarithms by multiplying their arguments. This property is key when working with ln expressions. Can you think of any applications in science or engineering where natural logarithms are commonly used?

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