To rewrite the expression \( \log m - 2\log p \) using the Quotient Rule of Logarithms, we need to apply the properties of logarithms.
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Using the Power Rule: First, we can rewrite \( 2\log p \) using the power rule. The power rule states that \( k \log b = \log(b^k) \), so: \[ 2\log p = \log(p^2) \]
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Using the Quotient Rule: The Quotient Rule states that \( \log a - \log b = \log\left(\frac{a}{b}\right) \). So now we can apply this to \( \log m - \log(p^2) \): \[ \log m - \log(p^2) = \log\left(\frac{m}{p^2}\right) \]
Thus, \( \log m - 2\log p \) can be rewritten as \( \log\left(\frac{m}{p^2}\right) \).
None of the provided options match \( \log\left(\frac{m}{p^2}\right) \). However, if we look closely, none of them properly represent the expression in the rewritten form from the Quotient Rule.
Therefore, none of the options can be considered correct.
If you can verify or provide additional context about the options, I can help select or deduce further!