Shading a horizontal region in (LogLog)Plot

Question

I would like to shade a horizontal region in LogLogPlot as in the figure below. The figure on the left is done with LogLogPlot:

LogLogPlot[x^2, {x, 10^-10, 10^5}, Frame -> True, GridLines -> Automatic, GridLinesStyle -> Directive[Dashed, LightGray], PlotLegends -> Placed[LineLegend[{Automatic}, {"y=\!\(\*SuperscriptBox[\(x\), \ \(2\)]\)"}], {.88, .15}]]

I am able to achieve the desired effect (figure on the right) by combining the plot with a RegionPlot:

f1 = Plot[Log[10, (10^xvar)^2], {xvar, -10, 5}, Axes -> False];
f2 = RegionPlot[-4 < xvar < 1, {xvar, -10, 5}, {yvar, -21, 11}, BoundaryStyle -> None, PlotStyle -> Directive[Antialiasing -> True, Hue[1, .6, 1, .3]], PlotLegends -> Placed[LineLegend[{Automatic}, {"y=\!\(\*SuperscriptBox[\(x\), \ \(2\)]\)"}], {.88, .12}]];
xticks = Table[{x, Superscript[10, ToString[x]]}, {x, -10, 5, 3}];
yticks = Table[{x, Superscript[10, ToString[x]]}, {x, -21, 11, 10}];
Show[{f1, f2}, Frame -> True, GridLines -> Automatic, GridLinesStyle -> Directive[Dashed, LightGray], Epilog -> {Text[Style["Awesome region", Hue[1, .5, .8]], Scaled[{0.54, 0.8}]]}, FrameTicks -> {{yticks, None}, {xticks, None}}]

However, this seems like a very inefficient way of doing such a simple thing as I have to map the logarithmic scales (because RegionPlot doesn't support log scales) and then map the ticks to get the right labels. Surely there must be a way of doing this in LogLogPlot directly.

Answer 1

Try this:

Show[{
  LogLogPlot[x^2, {x, 10^-10, 10^5}, Frame -> True, 
   GridLines -> Automatic, 
   GridLinesStyle -> Directive[Dashed, LightGray], 
   PlotLegends -> 
    Placed[LineLegend[{Automatic}, {"y=\!\(\*SuperscriptBox[\(x\), \ \
\(2\)]\)"}], {.88, .15}]],

  LogLogPlot[10^12, {x, 10^-4, 5}, PlotRange -> {10^-21, 10^12}, 
   Filling -> Bottom, FillingStyle -> Directive[Pink, Opacity[0.5]]]
  }]

Have fun!