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2lg2+lg25%lg10怎么算

(lg2)^2+lg5lg20-1 =(lg2)^2+lg5(2lg2+lg5)-1 =(lg2)^2+2lg2lg5+(lg5)^2-1 =(lg2+lg5)^2-1 =(lg10)^2-1 =1-1 =0

原式= 2/3*5/3*(lg3/lg2 * lg2/lg3) = 10/9 *(lg3*lg2 /(lg3*lg2) ) =10/9

应该是(lg2)^2+lg2*lg5+lg5 吧. (lg2)^2+lg2*lg5+lg5 =(lg2)^2+lg2*lg(10/2)+lg(10/2) =(lg2)^2+lg2*(lg10-lg2)+lg10-lg2 =(lg2)^2+lg2*(1-lg2)+ 1-lg2 =(lg2)^2 +lg2 -(lg2)^2+ 1-lg2 =1.

=lg2*lg(25*100)=lg2*(lg25+lg100)=lg2*(lg(5*5)+2)=lg2*(2lg(10/2)+2)=lg2*[2(lg10-lg2)+2]=lg2*[2(1-lg2)+2]=lg2*(4-2lg2)=4lg2-2(lg2)^2

lg5·lg20+lg2·lg2 =lg5·lg(2*10)+lg2·lg2 =lg5·(lg2+lg10)+lg2·lg2 =lg5·lg2+lg5+lg2·lg2 =lg2(lg5+lg2)+lg5 =lg2·lg10+lg5 =lg2+lg5 =lg10 =1

(lg5)^2+2lg2-(lg2)^2 = (lg5)^2-(lg2)^2+2lg2 =(lg5+lg2)(lg5-lg2)+2lg2 =lg10·(lg5-lg2)+2lg2 =lg5-lg2+2lg2 =lg5+lg2 =lg10 =1

如图

1/2lg25+lg2-lg根号0.1-log2(9)*log3(2) =1/2*lg(5^2)+lg2-lg[10^(-1/2)]-log2(9)*log3(2) 根据对数公式,积的对数等于对数的和,商的对数等于对数的差,还有换底公式 =1/2*2*lg5+lg2-(-1/2)*lg10-[log3(9)/log3(2)]*log3(2) =lg5+lg2+1/2-log3(9) ...

6lg2/3 -4lg10/9 +2lg25/6 =6lg2-6lg3-4lg10+4lg9+2lg25-2lg6 =6lg2-6lg3-4+8lg3+4lg5-2lg3-2lg2 =4lg2+4lg5-4 =4一4 =0

设 x = lg2 ,则 10^x = 2 , 因此 10^lg2 = 10^x = 2 。

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