Question

高中数学题目 关于对数lg25+(2/3)lg8+lg5·lg20+lg²2 需要详细的解答,麻烦给我思路 谢谢

Answer 1

lg25+(2/3)lg8+lg5·lg20+lg22

=lg5^2+(2/3)lg2^3+lg5*lg(5×2^2）+lg2*lg2

=2lg5+3*(2/3)lg2+lg5(lg5+2lg2)=lg2*lg2

=2lg5+2lg2+lg5*lg5+2lg2lg5+lg2*lg2

=2(lg5+lg2)+(lg2+lg5)^2

=2lg10+(lg10)^2

=2+1=3