a)
$3log_{\frac{1}{2}}16-2=log_{\frac{1}{2}}16^3-log_{\frac{1}{2}}(\frac{1}{2})^2=log_{\frac{1}{2}}(2^4)^3-log_{\frac{1}{2}}2^{-2}=log_{\frac{1}{2}}(2^{12}:2^{-2})=$$log_{\frac{1}{2}}2^{12-(-2)}=log_{\frac{1}{2}}2^{14}=log_{\frac{1}{2}}(\frac{1}{2})^{-14}=-14$
b)
log_432-3log2=log_432-log_42^3=log_4(32:8)=log_44=1
c)
log_5\frac{1}{4}+log_5100=log_5(\frac{1}{4}*100)=log_525=log_55^2=2
d)
log_33\sqrt3=log_33^1*3^{\frac{1}{2}}=log_33^{\frac{2}{2}+\frac{1}{2}}=log_33^{\frac{3}{2}}=\frac{3}{2}