Which of the following options correctly rewrites log m−2 log p

Question

using the Quotient Rule of Logarithms?

Option #1: log (m/2p)


Option #2: 2 log( m/p)


Option #3: log (m/p^2)

Answer 1

To rewrite the expression \( \log m - 2 \log p \) using the Quotient Rule of Logarithms, we can follow these steps:

1. Start with the expression: \[ \log m - 2 \log p \]

2. We can use the Power Rule of Logarithms, which states that \( k \log a = \log a^k \). Applying this rule to \( 2 \log p \): \[ \log m - \log p^2 \]

3. Now we can apply the Quotient Rule of Logarithms, which states that \( \log a - \log b = \log \left( \frac{a}{b} \right) \): \[ \log m - \log p^2 = \log \left( \frac{m}{p^2} \right) \]

So, the correct choice from the given options is:

Option #3: \( \log \left( \frac{m}{p^2} \right) \).