Question

一道高中数学对数函数题

lg5lg20-lg2lg50-lg25=?
要详细过程。。。

Answer 1

lg5lg20-lg2lg50-lg25
=lg5lg2*10-lg2lg5*10-lg5^2
=lg5(lg2+lg10)-lg2(lg5+lg10)-2lg5
=lg2lg5+lg5-lg2lg5-lg2-2lg5
=-lg2-lg5
=-(lg2+lg5)
=-lg10
=-1

Answer 2

lg5lg20 - lg2lg50 - lg25
= (1 - lg2)(lg10 + lg2) - lg2(lg100 -lg2) - (lg100 - lg4)
= (1 - lg2)(1 + lg2) - lg2(2 - lg2) -(2 - 2lg2)
= 1 - lg²2 - 2lg2 + lg²2 - 2 + 2lg2
= -1