高一对数运算.(1)lg25+(lg2)^2+lg2*lg5(2)lg2*lg50+lg5*lg20-lg100*lg5

(1)lg25+(lg2)^2+lg2*lg50
=2lg5+(lg2)^2+lg2(lg5+lg10)
=2lg5+(lg2)^2+lg2lg5+lg2
=2lg5+lg2(lg2+lg5)+lg2
=2lg5+lg2(lg2*5)+lg2
=2lg5+2lg2
=2lg(2*5)
=2
(2)lg2*lg50+lg5*lg20-lg100*lg5*lg2
=lg2*(lg5+lg10)+lg5*(lg2+lg10)-2lg2*lg5
=lg2*lg5+lg2+lg2*lg5+lg5-2lg2*lg5
=lg2+lg5
=lg(2*5)=1
(3)(log2 5+log4 0.2)*(log5 2+log25 0.5)
=(log2 5+(-0.5)log5 2)*(log5 2+(-0.5)log5 2)
=0.5log2 5*0.5log5 2=1/4

有个公式
lga+lgb=lga*b
logab=lgb/lga(logab中a为底数)

lg10=log10的10次也就是1

用计算器 一下就出来了

(1)lg25+(lg2)^2+lg2*lg50
＝（lg2）^2＋lg2*（lg2＋2lg5）＋2lg5
＝2（lg2）^2＋2lg2*lg5＋2lg5
＝2lg2（lg2＋lg5）＋2lg5
＝2lg2＋2lg5
＝2lg10＝2