Problem 18 - College Algebra

Question

In Exercises \(1-40,\) 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 expression of \(\log M^{-8}\) is \(-8 \cdot \log M\).

Step 1: Identify and Apply Applicable Logarithmic Properties

Looking at the expression, it can be seen that the base \(M\) has an exponent of -8. This aligns with the 'power rule' of logarithms, allowing the exponent to be brought in front of the logarithm.

Step 2: Applying the Power Rule

Using the power rule of logarithms, \(\log M^{-8}\) can be written as \(-8 \cdot \log M\).