How to draw this region plot in log scale

Questions
1

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)]
2

Are you sure you mean x^1/2 and not x^(1/2)?

3

Do the answers to RegionPlot with LogScale help you?