缚芸术:lg^3(2)+lg^3(5)+3lg(2)*lg(5)化简

来源:百度文库 编辑:高考问答 时间:2024/04/19 06:30:15

lg^3(2)+lg^3(5)+3lg(2)*lg(5)
=(lg(2)+lg(5))(lg^2(2)+lg^2(5)-lg(2)*lg(5))+3lg(2)*lg(5) (分解lg^3(2)+lg^3(5))
=lg^2(2)+lg^2(5)+2lg(2)*lg(5)
=(lg(2)+lg(5))^2
=1

lg^3(2)+lg^3(5)+3lg(2)*lg(5)
=(lg2+lg5)^3-3lg^2(2)lg(5)-3lg2lg^2(5)+3lg2lg5
=1-3lg^2(2)*lg(5)*(lg2+lg5-1)
=1-0=1