Question

Calculati: $log_6 \frac{ \sqrt[3]{36}}{216}$

Answer 1

[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]