lg2+lg5=?1-lg2=?1-lg5=?2lg5+2/3lg8+lg5*lg20+(lg2)2=?
问题描述:
lg2+lg5=?1-lg2=?1-lg5=?2lg5+2/3lg8+lg5*lg20+(lg2)2=?
答
lg2+lg5=lg2*5=lg10=1
1-lg2=lg10-lg2=lg(10/2)=lg5
2lg5+2/3lg8+lg5*lg20+(lg2)^2=2lg(10/2)+2/3lg(2^3)+lg(10/2)*lg(10*2)+(lg2)^2
=2-2lg2+2lg2+(1-lg2)(1+lg2)+(lg2)^2
=2+1-(lg2)^2+(lg2)^2
=3