a)
log_6\frac{1}{6}+log\sqrt[3]{10}=log_66^{-1}+log10^{\frac{1}{3}}=-1+\frac{1}{3}=\frac{-3+1}{3}=-\frac{2}{3}
b)
log_9\sqrt3-log_3\sqrt[4]{3}=log_93^{\frac{1}{2}}-log_33^{\frac{1}{4}}=log_9(\sqrt9)^{\frac{1}{2}}-\frac{1}{4}=log_9(9^{\frac{1}{2}})^{\frac{1}{2}}-\frac{1}{4}=
=log_99^{\frac{1}{4}}-\frac{1}{4}=\frac{1}{4}-\frac{1}{4}=0
c)
log_{\frac{2}{3}}1,5-log_{1,5}\frac{8}{27}=log_{\frac{2}{3}}\frac{3}{2}-log_{1.5}(\frac{2}{3})^3=log_{\frac{2}{3}}(\frac{2}{3})^{-1}-log_{\frac{3}{2}}(\frac{3}{2})^{-3}=
=-1-(-3)=-1+3=2
d)
log_2(3+log10)=log_2(3+1)=log_24=log_22^2=2log_22=2
e)
log_2(log\sqrt{10})=log_2(log10^{\frac{1}{2}})=log_2(\frac{1}{2})=log_22^{-1}=-1
f)
{log10^5+log_{0,1}100=5log10+log_{0,1}10^2=5+log_{\frac{1}{10}}(\frac{1}{10})^{-2}=5+(-2)=5-2=3}