In Prism's built-in variable slope dose-response curve, why is the HillSlope exponent applied to not only the X values (log concentration) but also the logEC50?

The equation is:

Y=Bottom + (Top-Bottom) / (1 + 10 ^ ((LogEC50-X)*HillSlope)

If you simplify this, remembering that X is log(Conc), the equation becomes (but don't use this form for fitting):

Y=Bottom + (Top-Bottom) / (1 + (EC50^HillSlope)/(Conc^HillSlope))

Why are both the EC50 and the concentration taken to the HillSlope power? Why not:

Y=Bottom + (Top-Bottom) / (1 + EC50 /(Conc^HillSlope))

You can write the equation either way. The best-fit curve will be identical, but the parameter values will differ. The best fit value of the "EC50" will be very different and, in fact,  it is not the value of X when Y is halfway between min and max. I found an enzyme kinetic book that does it the second way. But it doesn't fit "EC50", instead it fits "K". And then says that K equals EC50 to the HillSlope power,which makes it equivalent. Of course, you can enter any equation you like into Prism. There is no need to stick with our built-in equations.