总述：本次共解6题。其中
           ☆算术计算6题

〖1/6算式〗
    作业：求算式 (lg0.125-lg125)/1000^(-1/3) 的值.
    题型：数学计算
    解:
          (lg0.125-lg125)/1000^(-1/3)
        =-3/1000^(-1/3)
        =-3/1000^(-0.333333)
        =-3/0.100000230258774
        =-29.999931
    答案:(lg0.125-lg125)/1000^(-1/3)=-29.999931
〖2/6算式〗
    作业：求算式 log(2,0.5)+log(0.5,4)+log(sqrt2,2) 的值.
    题型：数学计算
    解:
          log(2,0.5)+log(0.5,4)+log(sqrt2,2)
        =-1+log(0.5,4)+log(sqrt2,2)
        =-1+(-2)+log(sqrt2,2)
        =-1+(-2)+1.999998
        =-3+1.999998
        =-1.000002
    答案:log(2,0.5)+log(0.5,4)+log(sqrt2,2)=-1.000002
〖3/6算式〗
    作业：求算式 3*log(7,2)-log(7,9)+2*log(7,3*sqrt2/4) 的值.
    题型：数学计算
    解:
          3*log(7,2)-log(7,9)+2*log(7,3*sqrt2/4)
        =3*0.356207-log(7,9)+2*log(7,3*sqrt2/4)
        =3*0.356207-1.12915+2*log(7,3*sqrt2/4)
        =3*0.356207-1.12915+2*0.030265
        =1.068621-1.12915+2*0.030265
        =1.068621-1.12915+0.06053
        =-0.060529+0.06053
        =0.000001
    答案:3*log(7,2)-log(7,9)+2*log(7,3*sqrt2/4)=0.000001
〖4/6算式〗
    作业：求算式 (lg8+lg125-lg2-lg5)/(lg(sqrt10)*lg0.1) 的值.
    题型：数学计算
    解:
          (lg8+lg125-lg2-lg5)/(lg(sqrt10)*lg0.1)
        =2/(lg(sqrt10)*lg0.1)
        =2/(lg3.162278*lg0.1)
        =2/(-0.5)
        =-4
    答案:(lg8+lg125-lg2-lg5)/(lg(sqrt10)*lg0.1)=-4
〖5/6算式〗
    作业：求算式 3^(1+log(3,6))-2^(4+log(2,3))-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1) 的值.
    题型：数学计算
    解:
          3^(1+log(3,6))-2^(4+log(2,3))-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)
        =3^(1+1.63093)-2^(4+log(2,3))-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)
        =3^2.63093-2^(4+log(2,3))-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)
        =3^2.63093-2^(4+1.584963)-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)
        =3^2.63093-2^5.584963-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)
        =3^2.63093-2^5.584963-lg2.236068+sqrt((lg(sqrt2))^2-lg2+1)
        =3^2.63093-2^5.584963-lg2.236068+sqrt((lg1.414214)^2-lg2+1)
        =3^2.63093-2^5.584963-lg2.236068+sqrt(0.150515^2-lg2+1)
        =3^2.63093-2^5.584963-lg2.236068+sqrt0.721625
        =3^2.63093-2^5.584963-0.349485+sqrt0.721625
        =3^2.63093-2^5.584963-0.349485+0.849485
        =18.000004873130315-2^5.584963-0.349485+0.849485
        =18.000004873130315-48.000016611541575-0.349485+0.849485
        =-30.000012-0.349485+0.849485
        =-30.349497+0.849485
        =-29.500012
    答案:3^(1+log(3,6))-2^(4+log(2,3))-lg(sqrt5)+sqrt((lg(sqrt2))^2-lg2+1)=-29.500012
〖6/6算式〗
    作业：求算式 lg2*lg50+lg5*lg20-lg100*lg5*lg2 的值.
    题型：数学计算
    解:
          lg2*lg50+lg5*lg20-lg100*lg5*lg2
        =0.30103*lg50+lg5*lg20-lg100*lg5*lg2
        =0.30103*1.69897+lg5*lg20-lg100*lg5*lg2
        =0.30103*1.69897+0.69897*lg20-lg100*lg5*lg2
        =0.30103*1.69897+0.69897*1.30103-lg100*lg5*lg2
        =0.30103*1.69897+0.69897*1.30103-2*lg5*lg2
        =0.30103*1.69897+0.69897*1.30103-2*0.69897*lg2
        =0.30103*1.69897+0.69897*1.30103-2*0.69897*0.30103
        =0.511441+0.69897*1.30103-2*0.69897*0.30103
        =0.511441+0.909381-2*0.69897*0.30103
        =0.511441+0.909381-1.39794*0.30103
        =0.511441+0.909381-0.420822
        =1.420822-0.420822
        =1
    答案:lg2*lg50+lg5*lg20-lg100*lg5*lg2=1

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