=lg5*(1+lg2)/(1/2)+2*(lg2)^2+2/3
=2lg5(1+lg2)+2*(lg2)^2+2/3
=2(1-lg2)(1+lg2)+2*(lg2)^2+2/3
=2-2(lg2)^2+2(lg2)^2+2/3
=8/3