d)
{log_5\frac{25\sqrt[3]{5}}{\sqrt[4]{125}}=log_5\frac{5^2*5^{\frac{1}{3}}}{\sqrt[4]{5^3}}=log_5\frac{5^{\frac{7}{3}}}{5^{\frac{3}{4}}}=log_5\frac{5^{\frac{28}{12}}}{5^{\frac{9}{12}}}=log_55^{\frac{19}{12}}=\frac{19}{12}=1\frac{7}{12}}
e)
log_{\frac{1}{4}}\frac{2\sqrt[5]{64}}{\sqrt{8}}=x
(\frac{1}{4})^x=\frac{2\sqrt[5]{64}}{\sqrt{8}}
(\frac{1}{2})^{2x}=\frac{2*\sqrt[5]{2^6}}{\sqrt{2^3}}
2^{-2x}=\frac{2^1*2^{\frac{6}{5}}}{2^{\frac{3}{2}}}
2^{-2x}=\frac{2^{\frac{11}{5}}}{2^{\frac{3}{2}}}
2^{-2x}=2^{\frac{22-15}{10}}
-2x=\frac{7}{10} \ |:(-2)
x=\frac{7}{10}*(-\frac{1}{2})
x=-\frac{7}{20}
log_{\frac{1}{4}}\frac{2\sqrt[5]{64}}{\sqrt{8}}=-\frac{7}{20}
f)
log_6\frac{\sqrt[3]{36}}{216}=log_6\frac{6^{\frac{2}{3}}}{6^3}=log_66^{\frac{2}{3}-\frac{9}{3}}=log_66^{-\frac{7}{3}}=-\frac{7}{3}