1.[log2(5)+log4(0.2)][log5(2)+log25(0.5)]
=[log2(5)+0.5log2(0.2)][log5(2)+0.5log5(0.5)]
=[log2(5*0.2^0.5)][log5(2*0.5^0.5)]
=lg(5^0.5)/lg2*lg(2^0.5)/lg5
=log5(5^0.5)*log2(2^0.5)=0.5*0.5=0.25
2.原式=lg5/lg15*lg45/lg15+(lg3/lg15)^2
=(lg5*lg45+lg3*lg3)/(lg15*lg15)
=[lg5*(lg5+2lg3)+lg3*lg3]/[(lg3+lg5)^2]
=[lg5*lg5+2lg3*lg5+lg3*lg3]/[(lg3+lg5)^2]
=[(lg5+lg3)^2]/[(lg3+lg5)^2]
=1
3.原式=(lg2)^2+2lg2*lg5+(lg5)^2
=(lg2+lg5)^2=(lg10)^2=1^2=1
