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[tex]\log_6{ \frac{ \sqrt[3]{36}}{216} } = log_6{ \frac{36^{ \frac{1}{3} }}{6^3} } \\\\ log_6{ \frac{6^{ \frac{2}{3} }}{6^3} } = log_6{6^{ \frac{2}{3}-3 }} \\\\ =log_6{6^{ \frac{-7}{3} }}\\\\ = \frac{-7}{3} log_6{6} \\\\ = \frac{-7}{3}[/tex]

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