1.lg²5+lg2×lg5+lg2
=lg5(lg5+lg2)+lg2
=lg5*lg(5*2)+lg2
=lg5+lg2
=1
2.（lg2）³ +（lg 5）³ +3lg 2×lg 5
=(lg2+lg5)(lg²2-lg2*lg5+lg²5)+3lg 2×lg 5
=lg²2+2lg2*lg5+lg²5
=(lg2+lg5)²
=1
3.7 的lg20次方×(1/2)的lg0.7次方
＝7 的(lg2*10)次方×(1/2)的(lg7*0.1)次方
=7 ^(1+lg2)×(1/2)^(-1+lg7)
=7*2*7^lg2*(1/2)^lg7
=14*7^lg2/2^lg7
4.lg500+lg8/5-1/2lg64+50(lg2+lg5)²
=lg500+lg8/5-lg8+50
=lg(500*8/5/8)+50
=lg100+50
=52