${\log ^{16}} = 1/204 \Rightarrow {\log ^{{2^4}}} = 1/204 \Rightarrow $$4{\log ^2} = 1/204 \Rightarrow {\log ^2} = \frac{{1/204}}{4} = 0/301$${\log ^{\frac{{\sqrt[3]{{25}}}}{2}}} = {\log ^{\frac{{\sqrt[3]{{{5^2}}}}}{2}}} = {\log ^{{{\frac{5}{2}}^{\frac{2}{3}}}}} = {\log ^{{5^{\frac{2}{3}}}}} - {\log ^2}$$ = \frac{2}{3}{\log ^5} - {\log ^2} = \frac{2}{3}\left( {1 - {{\log }^2}} \right) - {\log ^2} = $$\frac{2}{3}\left( {1 - 0/301} \right) - 0/301 = 0/466 - 0/301 = 0/165$