Problem 107 - College Algebra

Question

Describe the power rule for logarithms and give an example.

Step-by-Step Solution

Answer

The power rule for logarithms states that \(log_b (a^n) = n log_b (a)\). A practical example is \(log_3 (9^2) = 2 log_3 (9)\)

Step 1: Describe the Power Rule

The power rule of logarithms states that for any base \(b\), \(log_b (a^n) = n log_b (a)\). This means that when a number inside the log is raised to a power, we can take the power out and multiply it with the logarithm.

Step 2: Provide an example using the Power Rule

Let's demonstrate how to apply the power rule using the logarithm \(log_3 (9^2) = 2 log_3 (9)\). The original logarithm has the number 9 raised to the power of 2. According to the Power Rule, we can take this power out and multiply it with the logarithm, resulting in \(2 log_3 (9)\).