[?] Make filling from vertical epilog line to the y axis in LogLogPlot?

Questions
1

Hi,
I would like to ask for help on how color everything to the right of a vertical line in a LogLogPlot? From the line to the right y axis.
I made the following:

LogLogPlot[x^2, {x, 0, 2 Pi}, PlotRange -> {{0.001, 5}, {10^-4, 10}}, 
 Epilog -> Line[{{Log[1], Log[10^-4]}, {Log[1], Log[10]}}], 
 Frame -> True]

I need to exclude all the area from x=1 and to the right, and therefore shade it. I tried with filling but it did not produce anything, and I also tried to make a rectangle using graphics rectangle, but it can not show together with my LogLogPlot.

Thank you in advance,

2

Something like this?

Fig.png
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3

OK!

LogLogPlot[x^2, {x, 0, 2 Pi}, PlotRange -> {{0.001, 5}, {10^-4, 10}}, 
 Epilog -> {Gray, Opacity[.5], 
   Table[Line[{{Log[x0], Log[10^-4]}, {Log[x0], Log[10]}}], {x0, 1, 
     2*Pi, .01}]}, Frame -> True]
4

Thank you so much! That makes sense and works perfectly!

5

Thank you!

6

LogLogPlot[x^2, {x, 0, 2 Pi},
Prolog → {LightGray,
Rectangle[{Log1, Log[10^-4]}, {Log[5], Log[10]}]}, Frame → True,
PlotRange → {{0.001, 5}, {10^-4, 10}}]
This is a simple solution with Rectangle.

image.png
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