Problem 18 - 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. $$\log M^{-8}$$

Step-by-Step Solution

Answer

The expanded form of \( \log M^{-8} \) is \( -8 \log M \)

Step 1: Identify the logarithmic property to use

According to logarithmic properties, we can rewrite \( \log M^{-8} \) as \( -8 \log M \) because we can bring negative exponent out in front as a coefficient.

Step 2: Apply the logarithmic property

Using this property, we can simplify the given log expression to \( -8 \log M \).