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
2个回答

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