Interactions of Show and PlotRange for ListLogPlot

Question

Doing some Log plots and seeing odd interactions with Show and PlotRange

Simple example

ListLogPlot[{Range[100], Range[100]^2}\[Transpose]];
Show[%, PlotRange -> {1, 5}];
Grid[{{%%, %}}]

I would have expected the plot range on the righthand plot to be (1,5) not (Exp(1), Exp(5))

Is this expected? If so it seems wrong to me.

Answer 1

Yes, it is somehow expected. The result of ListLogPlot is a Graphics:

data = Transpose[{Range[100], Range[100]^2}]
(* {{1, 1}, {2, 4}, {3, 9}, {4, 16}, ...} *)

plot = ListLogPlot[data, PlotRange -> {{1, 100}, {1, 10}}];

plot // InputForm
(* Graphics[..., 
     Point[{{1., 0.}, {2., 1.3862943611198906}, 
            {3., 2.1972245773362196}, {4., 2.772588722239781}, 
            {5., 3.2188758248682006}, {6., 3.58351893845611} ...},
     PlotRange -> {{1., 100.}, {0., 2.302585092994046}}, ...] *)

Graphics uses the regular cartesian coordinates, and it was a ListLogPlot's job to convert your data points and PlotRange to the log scale, which you can see by observing the coordinates inside Point and the resulting PlotRange.

Therefore, when you alter the PlotRange within Show, you are not working in the original coordinate system of your data anymore, but in this transformed one.