(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)

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(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)(log5(10))^3-(lo

(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)
(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)

(log5(10))^3-(log5(2))^3-3log5(10)*log2(5)
令a=log5(10),b=log5(2)
则a-b=log5(10/2)=log5(5)=1
原式=a^3-b^3-3ab
=(a-b)(a^2+ab+b^2)-3ab
=1*(a^2+ab+b^2)-3ab
=a^2+ab+b^2-3ab
=a^2-2ab+b^2
=(a-b)^2
=1^2
=1

1-3log2(10)