数学对数函数化简求值题lg 5(lg 8+lg1000)+(lg 2^√3)^2+lg (1/6)+lg 0.06

解lg 5(lg 8+lg1000)+(lg 2^√3)^2+lg (1/6)+lg 0.06
=lg 5(3lg 2+3)+(√3lg 2)^2+lg (1/6)+lg 0.06
=lg 5(3lg 2+3)+3（lg 2)^2+lg[ (1/6)×(6/100)]
=3lg 5lg 2+3lg 5+3（lg 2)^2+lg[ (1/100)]
=3lg 5lg 2+3lg 5+3（lg 2)^2+lg[ (10)^(-2)]
=3(lg 5lg 2+lg 5+（lg 2)^2)-2
=3(lg 5lg 2+（lg 2)^2+lg 5)-2
=3[lg 2(lg 5+lg 2)+lg 5)-2
=3[lg 2(lg 10)+lg 5]-2
=3(lg 2+lg 5)-2
=3lg（10）-2
=3-2
=1

=3lg5(lg2+lg10)+3(lg2)^2-lg6+lg6-2lg10
=3(lg5lg2+lg5lg10+lg2lg2)-2lg10
=3(lg2lg10+lg5lg10)-2lg10
=3(lg10)^2-2lg10
=3-2
=1