How to label ticks in ListLogLogPlot in scientific form in MMA 10.4?

Question

This is a question regarding ListLogLogPlot in MMA 10.4. I have tried the solutions suggested in 5369, and they do not appear to work in MMA 10.4, so I would be grateful if this could be considered a new question by the moderators.

Using LogPlot with no tick label formatting, one gets:

LogLogPlot[Log[x!+1], {x, 1, 10^5}, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}]

Custom labels for the ticks can be added with:

LogLogPlot[Log[x! + 1], {x, .1, 10^5}, PlotRange -> {{.1, 10^5}, 
  {10^-1, 10^6}}, Ticks -> {Table[{10^i, 10^Defer[Evaluate[i]]}, 
  {i, -1, 5}], Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 6}]}]

So far so good. Now with ListLogLogPlot, and no custom tick label formating, we get:

plist = {#, 1. Log[#! + 1]} & /@ {.1, .5, 1, 5, 10, 50, 100, 500, 
     1000, 5000, 10000, 50000, 100000};

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
  Joined -> True]

Now try the custom tick labels, identical to those used above with LogLogPlot:

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
  Ticks -> {Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 5}], 
  Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 6}]}, Joined -> True]

I have tried text labels in the {value,label} form without any luck. Post 5369 suggests a hack to modify the plot after generation, also no joy.

Thanks!

UPDATE - Looks like this has been fixed in Mathematica 11.0.

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
   Ticks -> {Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 5}], 
   Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 6}]}, Joined -> True]

Answer 1

Here is one way to convert the ticks into the desired format:

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, Joined -> True] /. 
 {v_, t_?NumberQ, l1_, {AbsoluteThickness[0.1]}} :> 
 {v, NumberForm[N@t, NumberFormat -> (Superscript[#2, #3] &), 
  ExponentFunction -> (# &)], l1, {AbsoluteThickness[0.1]}}

---

With ticks outside and explicitly setting the AxesOrigin to get axes that are more aligned:

f[s_Spacer | s_Superscript] := s

f[n_Real | n_Integer] := Superscript[10, Rationalize@Log10[n]]

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
  Joined -> True, AxesOrigin -> {0.1, 0.1}] /. {v_, t_, l1_, l2_} :> {v, f[t], -l1, l2}

Answer 2

I tested on 10.2 and 10.4. I recommend just using the tick labels from some other plot and overlaying the data using Show. With minimal changes to your example I got following proof of principle.

plist = {#, 1. Log[#! + 1]} & /@ {.1, .5, 1, 5, 10, 50, 100, 500, 
    1000, 5000, 10000, 50000, 100000};

Show[{LogLogPlot[0, {x, .1, 10^5}, 
   PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
   Ticks -> {Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 5}], 
     Table[{10^i, 10^Defer[Evaluate[i]]}, {i, -1, 6}]}], 
  ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
   Joined -> True]}]

Answer 3

Using custom tick labels still works, but one has to use the logarithmic label position, as this conversion is no longer done automatically for custom tick labels.

ListLogLogPlot[plist, PlotRange -> {{.1, 10^5}, {10^-1, 10^6}}, 
 Ticks -> {Table[{N@Log[10^i], Superscript[10, i]}, {i, -1, 5}], 
           Table[{N@Log[10^i], Superscript[10, i]}, {i, -1, 6}]}, 
 Joined -> True]