Scale label problem of multiple ListLogPlot graphs

Question

Consider the following code:

data1 = {{0.70, 0.05}, {0.71, 0.06}, {0.72, 0.07}};
data2 = {{0.72, 0.07}, {0.72, 0.08}, {0.72, 0.1}, {0.72, 0.2}, {0.72,0.4}, {0.73, 0.6},{0.73, 0.8}, {0.73, 1.0}, {0.73, 2.0}, {0.74, 4.0}, {0.74, 5.0}, {0.74, 6.0}, {0.75, 8.0},{0.78, 10.0}};
data3 = {{0.72, 0.07}, {0.74, 0.08}, {0.76, 0.1}, {0.84, 0.2}, {0.9, 0.4}, {0.96, 0.6}, {1.0, 0.8}, {1.02, 1.0}, {1.12, 2.0}, {1.22, 4.0}, {1.26, 5.0}};

sg = ListLogPlot[Tooltip[data1], Joined -> True, Mesh -> Automatic];
sl = ListLogPlot[Tooltip[data2], Joined -> True, Mesh -> Automatic];
lg = ListLogPlot[Tooltip[data3], Joined -> True, Mesh -> Automatic];
Show[sg, sl, lg, PlotRange -> All]

There is no problem with the individual plots but their scales mess up when I combine them using Show command.The scale label just simply disappear. Any idea on how to fix this?

Answer 1

From Docs>>Show>>Possible Issues

Show uses the options from the first graphic

In this case, the Ticks and/or FrameTicks options from the first graphic are used unless Show is provided explicit settings for this option. Since the PlotRange and FrameTicks settings for sg cover only a portion of the whole range for sl and lg, you see only the ticks/labels from sg when you use

  Show[sg, sl, lg, PlotRange -> All]

First, few changes in the code to distinguish the three plots when they are `Show'n together:

sg = ListLogPlot[Tooltip[data1], Joined -> True, Mesh -> Automatic, 
  PlotStyle -> Directive[Opacity[.5], Thin, Red]];
sl = ListLogPlot[Tooltip[data2], Joined -> True, Mesh -> Automatic, 
  PlotStyle -> Directive[Opacity[.5], Thickness[.01], Blue]];
lg = ListLogPlot[Tooltip[data3], Joined -> True, Mesh -> Automatic, 
  PlotStyle -> Directive[Opacity[.5], Thickness[.02], Green]];

Since the PlotRange and FrameTicks settings for sl are "more representative" (so to speak), changing the order of graphics in Show

Show[sl, sg, lg, PlotRange -> All, Frame -> True, AspectRatio -> 1]

gives

Alternatively, you could have the input graphics in any order but provide the settings for FrameTicks explicitly in Show to get the same result:

 Show[sg, sl, lg, PlotRange -> All, Frame -> True, AspectRatio -> 1, 
  FrameTicks -> (FrameTicks /. sl[[2]])] 

where I used the facts that

1. You can get the options (not all of them, btw) of a graphics object by looking into its second Part, that is sl[[2]] contains the option settings PlotRange, AxesLabel, FrameTicks ... etc for sl.
2. Using the replacement rule FrameTicks /. sl[[2]] we get the values of this option in sl.