Question

lg5(lg8+lg1000)+（lg2^√3）^2+lg1/6+lg0.06等于

Answer 1

lg5(lg8+lg1000)+（lg2^√3）^2+lg1/6+lg0.06
=lg5(lg8+lg1000)+(√3*lg2)^2+lg1/6+lg0.06
=lg5(3lg2+3)+3(lg2)^2+lg1-lg6+lg6-lg100
=3lg5 lg2+3lg5+3(lg2)^2-1
=3[lg5 lg2+lg5+(lg2)^2]-1
=3[(lg2+lg5)^2-(lg5)^2-lg2 lg5]-1
=3[-lg5(lg5+lg2)]-1
=-3lg5-1

Answer 2

原式=lg5(lg2³+lg10³)+(√3lg2)²+lg6^(-1)+lg(6/10²)
=lg5(3lg2+3)+3lg²2-lg6+lg6-lg10²
=3lg2lg5+3lg5+3lg²2-2
=3lg2(lg5+lg2)+3lg5-2
=3lg2+3lg5-2
=3(lg2+lg5)-2
=3-2
=1