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

Step-by-Step Solution

Answer

The expanded form of the given logarithmic expression \( \log N^{-6} \) is \( -6 \log N \)

Step 1: Understand the Power Rule of Logarithms

The power rule of logarithms states that \( \log_a(m^n) = n \log_a(m) \). This rule is used when there is a power in a logarithmic expression.

Step 2: Apply the Power Rule

Applying the power rule to the given expression \( \log N^{-6} \), we get \( -6 \log N \). Here, \( N \) is the base and -6 is the exponent.

Step 3: Examine the Result

The result \( -6 \log N \) is the expanded form of the original expression. Without specific value of N, we cannot further evaluate the expression. If the value of N is known, you can replace N in the expression and calculate the final result