Draw an exclusion plot using a set of inequalities(make a loglogregionplot)

Questions
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1

logLogRegionPlot[rplot_] := Module[{pts, pgon},
pts = Cases[Normal@rplot, Line[a__] :> a, Infinity];
pgon = {EdgeForm,
Directive[RGBColor[0.368417, 0.506779, 0.709798],
AbsoluteThickness[1.6], Opacity[0.3]],
Cases[Normal@rplot, Polygon[], Infinity]};
ListLogLogPlot[pts,
Joined → True,
Frame → True,
PlotRange → All,
AspectRatio → 1,
Axes → False,
PlotStyle → ColorData[1][1],
Epilog → (pgon /. {x, y_?NumericQ} :> Log@{x, y})]
]
logLogRegionPlot@RegionPlot[{y > 8*(10^-10)
(x)^(1/2)HeavisideTheta[(x)^(-1) - (y)] &&
x > 6(10^4) && x < 6*(10^10) &&
y < (8*(10^-10))^-1 x^(-5/2)HeavisideTheta[-(x)^(-1) +
(y)] &&
y > 0.6x^(-3/2)}, {x, 10^2, 10^14}, {y, 10^-16, 10^0},
PlotPoints → 100]

How can I produce an log region plot satisfying those inequalities, I have tried to produce it with the above code an exclusion region is coming, but I need a large plot range for which it is giving a wrong plot.

2

What do you mean by Boole?

3

Boole is similar like the HeavisideTheta function and it is used here to differentiate between two boundary conditions, to overcome the confusion I have now replaced it with straight forward HeavisideTheta