Question 298804
    lnx=ln(2x-1)-ln(x-2)
    lnx=ln(2x-1)/(x-2)
    x=(2x-1)/(x-2)
    x(x-2)=(2x-1)
    x^2-2x=2x-1
    x^2-4x=-1
    x^2-4x+1=0
Since we can't factor, we must resort to the quadratic formula.  Doing so yields:
x = {3.732, 0.268}
We can toss out 0.268 because if we use it in the original equation it produces a ln of a negative number -- toss it out, it is an extraneous solution.  This leaves:
x =  3.732
.
Details of quadratic formula to follow:
*[invoke quadratic "x", 1, -4, 1 ]