Correct Answer: Option B

Explanation

\(\frac{\log_{3} 27 - \log_{\frac{1}{4}} 64}{\log_{3} (\frac{1}{81})}\)

\(\log_{3} 27 = \log_{3} 3^{3} = 3\log_{3} 3 = 3\)

\(\log_{\frac{1}{4}} 64 = \log_{\frac{1}{4}} (\frac{1}{4})^{-3} = -3\)

\(\log_{3} (\frac{1}{81}) = \log_{3} 3^{-4} = -4\)

\(\therefore \frac{\log_{3} 27 - \log_{\frac{1}{4}} 64}{\log_{3} (\frac{1}{81})} = \frac{3 - (-3)}{-4}\)

= \(\frac{6}{-4} = \frac{-3}{2}\)

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