I have two equations from which I have to draw a region plot in Log scale,
1/y<3*10^-19*x^1/2*HeavisideTheta[x-(6*10^36/y)] y<10^55*x^-3/2*HeavisideTheta[-x+(6*10^36/y)]
Do the answers to RegionPlot with LogScale help you?
Are you sure you mean x^1/2 and not x^(1/2)?
x^1/2
x^(1/2)