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