Question

一道对数题^^

(log2)^3+(log5)^3+(log2)(log8)
(log2)^3+(log5)^3+(log5)(log8) *刚才的题目错了==

Answer 1

(lg2)^3+(lg5)^3+(lg5)(lg8)
=(lg2+lg5)^3-3(lg2)(lg5)^2-3(lg5)(lg2)^2+(lg5)(lg8)
=1-3(lg2)(lg5)^2-3(lg5)(lg2)^2+(lg5)(lg8)
=1-3(lg2)(lg5)[lg5+lg2]+(lg5)(lg8)
=1-3(lg2)(lg5)+3(lg5)(lg2)=1
(方法二)
(lg2)^3+(lg5)^3+(lg5)(lg8)
=(lg2)^3+(1-lg2)^3+(1-lg2)(3lg2)
=(lg2)^3+1-3lg2+3(lg2)^2-(lg2)^3+3lg2-3(lg2)^2
=1