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How can I do a region plot with its mesh function in Log scale?

For example,

xlabel = "B";
ylabel = "A";

test = 
  RegionPlot[A > B, {B, 10^-5, 0.1}, {A, 0.001, 0.1}, 
    Axes -> False, 
    Frame -> True, 
    FrameLabel -> {xlabel, ylabel}, 
    FrameStyle -> 
      Directive[Thickness[0.004], Bold, FontFamily -> "Times New Roman", Black, 12], 
    BoundaryStyle -> Directive[Brown, Thick, Dashed], 
    PlotStyle -> Transparent, 
    Mesh -> 20, 
    MeshStyle -> Directive[Brown, Dotted, Thickness[0.007]]];

Show[
  test /. 
    GraphicsComplex[c_, prims___] :> 
      GraphicsComplex[{Log @ #, Log @ #2} & @@@ c, prims],
  FrameTicks -> 
    {{Charting`ScaledTicks[{Log, Exp}], Charting`ScaledFrameTicks[{Log, Exp}]}, 
     {Charting`ScaledTicks[{Log, Exp}], Charting`ScaledFrameTicks[{Log, Exp}]}}, 
  PlotRange -> All, 
  ImageSize -> 300]

gives region plot in Log scale, but the mesh functions are modified too from the original one,

RegionPlot[A > B, {B, 10^-5, 0.1}, {A, 0.001, 0.1}, 
  Axes -> False, 
  Frame -> True, 
  FrameLabel -> {xlabel, ylabel}, 
  FrameStyle -> 
    Directive[Thickness[0.004], Bold, FontFamily -> "Times New Roman", Black, 12], 
    BoundaryStyle -> Directive[Brown, Thick, Dashed], 
  PlotStyle -> Transparent, 
  Mesh -> 20, 
  MeshStyle -> Directive[Brown, Dotted, Thickness[0.007]]]
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Use MeshFunction with logarithmic arguments.

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  • $\begingroup$ it is working now.. thanks $\endgroup$ – tdj Dec 30 '18 at 13:01

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