高一对数运算一道lg5²+2/3lg8+lg5*lg20+lg²2=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 07:03:51
高一对数运算一道lg5²+2/3lg8+lg5*lg20+lg²2=高一对数运算一道lg5²+2/3lg8+lg5*lg20+lg²2=高一对数运算一道lg5&

高一对数运算一道lg5²+2/3lg8+lg5*lg20+lg²2=
高一对数运算一道
lg5²+2/3lg8+lg5*lg20+lg²2=

高一对数运算一道lg5²+2/3lg8+lg5*lg20+lg²2=
原式=2lg5+2/3lg2^3+lg5*[lg(2*10)]+lg²2
=2lg5+2lg2+lg5(lg2+lg10)+lg2*lg2
=2(lg2+lg5)+lg5*lg2+lg5+lg2*lg2
=2lg10+lg2(lg5+lg2)+lg5
=2+lg2+lg5=2+lg10=3

lg5²+2/3lg8+lg5*lg20+lg²2
=2*lg5+lg8^(2/3)+lg5*lg(4*5)+(lg2)^2
=2lg5+lg4+lg5lg4+(lg5)^2+(lg2)^2
=2lg5+2lg2+2lg5lg2+(lg5)^2+(lg2)^2
=2*(lg5+lg2)+(lg5+lg2)^2
=2lg10+(lg10)^2=3

lg5²+2/3lg8+lg5*lg20+lg²2
=2lg5+2lg2+lg5(lg2+1)+lg²2
=2+l+lg5+lg²2
=3+1-lg2+lg²2
=4+lg2(lg2-1)
=4+lg2*(-lg5)
=4-1
=3