Math Example: Laws of Logarithms: Example 19

Topic

Logarithms

Description

This example demonstrates the simplification of the logarithmic expression log₂(2^7) + log₂(2¹⁰) using the power property of logarithms. The solution applies the rule log_n(n^a) = a to each term, resulting in 7 + 10, which simplifies to 17.

Logarithms with different bases are a crucial topic in mathematics, particularly in algebra and precalculus. These examples help students understand the properties of logarithms and how to manipulate logarithmic expressions involving exponents. 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 different bases and 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: Now, let's look at this example involving logarithms with base 2. We have log₂(2⁷) + log₂(2¹⁰). Remember the power rule of logarithms: when the base of the logarithm matches the base inside, we can simply bring down the exponent. So, log₂(2⁷) becomes 7, and log₂(2¹⁰) becomes 10. Now we just add these numbers: 7 + 10 = 17. This example shows how we can quickly simplify logarithmic expressions when the bases match, saving us time in more complex problems.

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