计算 (Log6 3)^2+【(log6 18)/(log2 6)]

2个回答

  • (log6 3)^2+【(log6 18)/(log2 6)]

    = (lg3/lg6)^2+[(lg18/lg6)/(lg6/lg2)]

    = (lg3/lg6)^2+(lg18/lg6)*(lg2/lg6)

    = (lg3/lg6)^2+(lg18*lg2/lg6*lg6)

    = (lg3/lg6)^2+[lg(9*2)*lg2/lg6*lg6)]

    = (lg3/lg6)^2+[(2lg3+lg2)*lg2/lg6*lg6)]

    = (lg3)^2/(lg6)^2+[2lg3*lg2+(lg2)^2]/(lg6)^2

    = [(lg3)^2+2lg3*lg2+(lg2)^2]/(lg6)^2

    = (lg3+lg2)^2/(lg6)^2

    =[ lg(3*2)]^2/(lg6)^2

    = (lg6)^2/(lg6)^2

    =1