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lg2lg50

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lg²5+lg2(lg5+lg10) =lg²5+lg2lg5+lg2 =lg5(lg5+lg2)+lg2 =lg5+lg2 =1

(lg5)²+lg2*lg50 =(lg5)²+lg2×(lg5+lg10) =(lg5)²+lg2lg5+lg2lg10 =lg5(lg5+lg2)+lg2 =lg5lg10+lg2 =lg5+lg2 =lg10 =1 明教为您解答, 如若满意,请点击[满意答案];如若您有不满意之处,请指出,我一定改正! 希望还您一个正确答复!...

(lg2)^2+lg2lg50+lg25=(lg2)^2+lg2(lg2*25)+lg25=(lg2)^2+lg2(lg2+lg25)+lg25=2(lg2)^2+lg2lg25+lg25=2(lg2)^2+2lg2lg5+2lg5=2lg2(lg2+lg5)+2lg5=2lg2+2lg5=2(lg2+lg5)=2(lg10)=2

由题,lg5lg20-lg2lg50-lg25=lg5(2lg2+lg5)-lg2(2lg5+lg2)-2lg5=lg25-lg22-2lg5=lg5-lg2-2lg5=-(lg2+lg5)=-1故答案为-1

(lg2)²+lg2lg50+lg25 =(lg2)²+lg2×lg(5²×2)+lg5² =(lg2)²+lg2(2lg5+lg2)+2lg5 =(lg2)²+(lg2)²+2lg2lg5+2lg5 =2lg2lg2+2lg2lg5+2lg5 =2lg2(lg2+lg5)+2lg5 =2lg2×lg10+2lg5 =2lg2+2lg5 =2(lg2+lg5) =2

lg2*lg50=lg2*(lg10+lg5)=lg2*(1+lg5)=lg2+1

(lg2)²+lg2·lg50+lg25= =(lg2)²+lg2·(1+lg5)+2lg5 =(lg2)²+lg2lg5+lg2+2lg5 =lg2(lg2+lg5)+lg2+2lg5 =lg2*lg10+lg2+2lg5 =lg2+lg2+2lg5 =2(lg2+lg5) =2lg10 =2

lg²5+lg2×lg50 =lg²5+lg2×lg(5²×2) =lg²5+lg2×(2lg5+lg2) =lg²5+2lg5lg2+lg²2 =(lg5+lg2)² =lg²(5×2) =1

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