化简：2lg5+2\3lg8+lg5*lg20+lg的平方2

化简：2lg5+2\3lg8+lg5*lg20+lg的平方2
化简：2lg5+2\3lg8+lg5*lg20+lg的平方2

化简：2lg5+2\3lg8+lg5*lg20+lg的平方2
2lg5+2\3lg8+lg5*lg20+lg的平方2
=2lg5+2\3lg2³+lg5*lg2*10+lg²2
=2lg5+2lg2+lg5（lg2+lg10）+lg²2
=2（lg5+lg2）+lg5（lg2+1）+lg²2
=2+lg5lg2+lg5+lg²2
=2+lg2（lg5+lg2）+lg5
=2+lg2+lg5
=3

2lg5＋(2/3)lg8＋lg5×lg20＋lg²2
=2lg5+(2/3)lg2³+lg5×lg(4×5)+lg²2
=2lg5+2lg2+lg5(2lg2+lg5)+lg²2
=lg²5+2lg5lg2+lg²2+2(lg5+lg2)
=(lg5+lg2)²+2(lg5+lg2)
=1+2
=3

2lg5+2\3lg8+lg5*lg20+(lg^2)2
=2lg5+2lg2+lg5*(lg(2*10))+(lg^2)2
=2(lg5+lg2)+lg5lg2+lg5+(lg^2)2
=2+(lg10-lg2)lg2+lg10-lg2+(lg^2)2
=2+lg2-(lg^2)2+1-lg2+(lg^2)2
=3