Problem 17 - 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. $$ \log N^{-6} $$

Step-by-Step Solution

Answer

The simplified form of \( \log N^{-6} \) is \(-6 \log N\)

Step 1: Recall the property of logarithms

Recall the property \( \log a^n = n \log a \). This property allows the possibility to move the exponent out in front of the logarithm.

Step 2: Apply the property on the given expression

Apply the mentioned property to the given logarithmic expression \( \log N^{-6} \). Therefore, it becomes \(-6 \log N\)

Step 3: Final simplified answer

The logarithm \( \log N^{-6} \) has been expanded and simplified to \(-6 \log N\)