log8 9*log3 2+lg5lg20+(lg2)^2
=lg9/lg8 * lg2/lg3 + lg5*(lg4+lg5)+(lg2)^2
=2lg3/(3lg2)* lg2/lg3 + 2lg5*lg2+(lg5)^2 +(lg2)^2
=2/3 +(lg5+lg2)^2
=2/3 +1
=5/3