一道整式题求解.log0.5x(x^2) - 14log16x(x^3) + 40log4x(根号下x)=0求xloga

5个回答

  • log2(x^2)/log2(0.5x)-14log2(x^3)/

    log2(16x)+40log2(x^0.5)/log2(4x)=0

    将原式都转换成以2为底的对数

    2log2(x)/[log2(0.5)+log2(x)]-42log2(x)/[log2(16)+log2(x)]+20log2(x)/[log2(4)+log2(x)]=0

    log2(x)/[-1+log2(x)]-21log2(x)/[4+log2(x)]+10log2(x)/[2+log2(x)]=0

    [log2(x)]{1/[-1+log2(x)]-21/[4+log2(x)]+10/[2+log2(x)]}=0

    通分

    [log2(x)]=0

    化简

    [log2(x)]=0

    [log2(x)][1+2log2(x)][-2+log2(x)]/[-1+log2(x)][4+log2(x)][2+log2(x)]=0

    所以:log2(x)=0或1+2log2(x)=0或-2+log2(x)=0

    解得:x=1;x=1/根号2;x=4