(2lg2+lg3)/(1+0.5lg36+1/3 lg8)
=(2lg2+lg3)/{1+0.5lg(6^2)+ lg[2^3^(1/3)]}
=(2lg2+lg3)/[1+(0.5*2)lg6+lg2]
=[lg(2^2)+lg3]/[1+lg6+lg2]
=(lg4+lg3)/[lg10+lg6+lg2]
=lg(4*3)/lg(10*6*2)
=lg12/lg120