a)
2log_36-log_34=log_36^2-log_34=log_336-log_34=log_3(36:4)=
=log_39=log_33^2=2
b)
log8+3log5=log8+log5^3=log8+log125=log(8*125)=
=log1000=log10^3=3
c)
log_43+2log_4\frac{2\sqrt3}{3}=log_43+log_4(\frac{2\sqrt3}{3})^2=log_43+log_4\frac{4*\not3^1}{\not9^3}=log_43+log_4\frac{4}{3}=log_4(\not3^1*\frac{4}{\not3^1})=log_44=1
d)
2log_{\frac{1}{2}}5+4log_{\frac{1}{2}}2-2log_{\frac{1}{2}}10=log_{\frac{1}{2}}5^2+log_{\frac{1}{2}}2^4-log_{\frac{1}{2}}10^2=
log_{\frac{1}{2}}25+log_{\frac{1}{2}}16-log_{\frac{1}{2}}100=log_{\frac{1}{2}}(25*16)-log_{\frac{1}{2}}100=log_{\frac{1}{2}}400-log_{\frac{1}{2}}100=
=log_{\frac{1}{2}}(400:100)=log_{\frac{1}{2}}4=log_{\frac{1}{2}}2^2=log_{\frac{1}{2}}(\frac{1}{2})^{-2}=-2
e)
log_33-3log_32+log_324=log_33-log_32^3+log_324=log_33-log_38+log_324=
=log_3\frac{3}{8}+log_324=log_3(\frac{3}{\not8^1}*\not24^3)=log_39=log_33^2=2
f)
log_{\frac{1}{4}}18+log_{\frac{1}{4}}8-2log_{\frac{1}{4}}3=log_{\frac{1}{4}}(18*8)-log_{\frac{1}{4}}3^2=log_{\frac{1}{4}}144-log_{\frac{1}{4}}9=
=log_{\frac{1}{4}}(144:9)=log_{\frac{1}{4}}16=log_{\frac{1}{4}}4^2=log_{\frac{1}{4}}(\frac{1}{4})^{-2}=-2
g)
log15+log2+2log5-log\frac{3}{4}=log(15*2)+log5^2-log\frac{3}{4}=log30+log25-log\frac{3}{4}=
=log(30*25)-log\frac{3}{4}=log750-log\frac{3}{4}=log(750:\frac{3}{4})=log(\not750^{250}*\frac{4}{\not3^1})=
=log1000=log10^3=3