Problem 2 - Introductory and Intermediate Algebra for College Students 4th

Question

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{8}(13 \cdot 7)$$

Step-by-Step Solution

Answer

The expanded expression is \(\log_8(13) + \log_8(7)\)

Step 1: Understand the Property

One of the properties of logarithms is that the log of a product is equal to the sum of the logs. This can be written as \(\log_b(mn) = \log_b(m) + \log_b(n)\)

Step 2: Apply the Property

Apply that property of logarithms to the given expression. Therefore, apply that rule to \(\log _{8}(13 \cdot 7)\) which means the expression can be expanded into \(\log_8(13) + \log_8(7)\)