Hi,

solve for x:

 ln(x-(1/2)) + ln2 = 2lnx

 ln(x-(1/2)) + ln2 - lnx^2 = 0

 ln 2(x-(1/2))/x^2  = 0

   

     2x - 1 = x^2

     x^2 - 2x - 1 = 0

   (x-1)(x-1) = 0,   

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