(lg5)2+1g2*1g25+(1g2)2对数运算,求详尽运算过程!

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(lg5)2+1g2*1g25+(1g2)2对数运算,求详尽运算过程!

(lg5)2+1g2*1g25+(1g2)2对数运算,求详尽运算过程!
(lg5)2+1g2*1g25+(1g2)2
对数运算,求详尽运算过程!

(lg5)2+1g2*1g25+(1g2)2对数运算,求详尽运算过程!
(lg5)2+1g2*1g25+(1g2)2
=(lg5)2+1g2*1g5^2+(1g2)2
=(lg5)2+21g2*1g5+(1g2)2
=(lg5+1g2)2
=1

(lg5)^2+1g2*1g25+(1g2)^2
=(lg5)^2+1g2*1g(5)^2+(1g2)^2
=(lg5)^2+21g2*1g5+(1g2)^2
=(lg5+lg2)^2
=(lg10)^2
=1

因为lg25=lg(5^2)=2lg5
所以原式=(lg5)^2+2(lg2)(lg5)+(lg2)^2
=(lg5+lg2)^2
=(lg10)^2
=1