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

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/13 18:13:49

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

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