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lg25+2/3lg8+lg5lg20+lg^22

lg25+(2/3)lg8+lg5lg20+lg^22=2lg5+2lg2+lg5*(2lg2+lg5)+lg2*lg2=2*(lg5+lg2)+2*lg5*lg2+(lg5)^2+(lg2)^2=2*lg(5*2)+(lg5+lg2)^2=2*lg(10)+(lg(5*2))^2=2+(lg(10))^2=2+1=3

lg25+2/3lg8+lg5lg20+lg2lg2=lg5+(2/3)lg2+lg5(lg2*10)+lg2lg2=2lg5+(2/3)*3lg2+lg5(lg2+lg10)+lg2lg2=2lg5+2lg2+lg5(lg2+1)+lg2lg2=2lg5+2lg2+lg5lg2+lg5+lg2lg2=2(lg5+lg2)+lg5lg2+lg2lg2+lg5=2(lg10)+lg2(lg5+lg2)+lg5=2+lg2(lg10)+lg5=2+lg2+lg5=2+lg(2*5)2+lg10=2+1=3

lg25+2/3lg8+lg5乘以lg20+lg^22=2lg5+2lg2+lg5*(2lg2+lg5)+lg2*lg2=2(lg5+lg2)+(lg5)^2+2lg2*lg5+(lg2)^2=2lg10+(lg5+lg2)^2=2+1^2=3

lg25+2/3lg8+lg20*lg5+(lg2)^2=2lg5+2lg2+(lg4+lg5)lg5+(lg2)^2=2lg5+2lg2+2lg2*lg5+(lg5)^2+(lg2)^2=2(lg5+lg2)+(lg2+lg5)^2=2lg10+(lg10)^2=2+1=3

lg25+2/3lg8+lg5*lg20+(lg^2)2 =2lg5+2lg2+lg5*(lg5+2lg2)+(lg2)^2 =2(lg5+lg2)+(lg5)^2+2lg5*lg2+(lg2)^2 =2lg(2*5)+(lg5+lg2)^2 =2*1+1 =3

lg25+2/3lg8+lg5*lg20+lg^22=2lg5+2lg2+lg5*(2lg2+lg5)+lg2*lg2=2(lg5+lg2)+(lg5)^2+2lg2*lg5+(lg2)^2=2lg10+(lg5+lg2)^2=2+1^2=3

解:原式= lg25+2/3lg8+lg5*lg20+(lg2) =2lg5 + 3*2/3*lg2 + lg5(lg2 + 1) +(lg2) = 2lg5 + 2lg2 + (1-lg2)(1+lg2) +(lg2) = 2lg10 + 1- (lg2) +(lg2) = 2+1 = 3

原式=2lg5+2lg2+lg5(lg4+lg5)+lg2=2(lg2+lg5)+lg5+2lg2*lg5+lg2=2+(lg5+lg2)=2+1=3

2\3lg8=lg 8^(2/3)=lg4所以上式等于lg25+lg4+lg5+(lg2)^2=lg(25*4)+lg5+(lg2)^2=2+lg5+(lg2)^2=2+lg(10*0.5)+(lg2)^2=3+lg0.5+(lg2)^2=3-lg2-(lg2)^2=3-lg2(1+lg2)=3-lg2*lg20

=(lg2)(lg2 lg50) lg25=(lg2)[lg(2*50)] lg25=(lg2)(lg100) lg25 =2*(lg2) 2*(lg5) =2(lg2 lg5) =2(lg(2*5)) =2lg10 =2;

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