a)
log_{ \sqrt{3}} 27 \sqrt[3]{9}=x
(\sqrt3)^x=27\sqrt[3]9
(3^{\frac{1}{2}})^x=3^3*(3^2)^{\frac{1}{3}}
3^{\frac{1}{2}x}=3^3*3^{\frac{2}{2}}
3^{\frac{1}{2}x}=3^{3\frac{2}{3}}
\frac{1}{2}x=3\frac{2}{3}
\frac{1}{2}x=\frac{11}{3}|*2
x=\frac{22}{3}=7\frac{1}{3}
----------
log_{ \sqrt{3}} 27 \sqrt[3]{9}=7\frac{1}{3}
b)
log_{ \frac{3}{2} } \frac{16}{81 }=log_{\frac{3}{2}}(\frac{2}{3})^4=log_{\frac{3}{2}}(\frac{3}{2})^{-4}=-4
c)
3^{2+ log_{3} 4}=3^{log_33^2+log_34}=3^{log_39+log_34}=3^{log_3(9*4)}=3^{log_336}=36