Scientific notations with negative powers for plotting

Question

Plot[x^2, {x, 0, 100}, 
 Ticks -> {{#, ScientificForm@#} & /@ 
    Range[0., 100., 30.], {#, ScientificForm@#} & /@ 
    Range[0., 100^2, 1000.]}, PlotRange -> All]

PowerTicks[label_][min_, max_] := 
  Block[{min10, max10}, min10 = Floor[Log10[min]];
   max10 = Ceiling[Log10[max]];
   Join[Table[{10^i, 
      If[label, Superscript[10, i], Spacer[{0, 0}]]}, {i, min10, 
      max10}], 
    Flatten[
     Table[{k 10^i, 
       Spacer[{0, 0}], {0.005, 0.`}, {Thickness[0.001`]}}, {i, min10, 
       max10}, {k, 9}], 1]]];

ListLogLogPlot[Range[20]^3, Frame -> True, 
 FrameTicks -> {{PowerTicks[True], 
    PowerTicks[False]}, {PowerTicks[True], PowerTicks[False]}}]

The above code works very well for the positive powers. Could some one please check it how does it change for the negative powers. More specific, on both axes the scales should be ranging {10^-5, 10^-4....10^0, 10^1, 10^2,...10^5}. Thanks!

Answer 1

The axes are scaled to the data. If only want to change the axes with the same data you may use PlotRange:

ListLogLogPlot[Range[20]^3, Frame -> True, 
 FrameTicks -> {{PowerTicks[True], 
    PowerTicks[False]}, {PowerTicks[True], PowerTicks[False]}}, 
 PlotRange -> {{10^-5, 10^5}, {10^-5, 10^5}}]

However, MMA does this automatically if the data span this range. E.g.:

dat = Join[(1/Range[40])^3, Range[40]^3];
dat = Transpose[{dat, dat}];
ListLogLogPlot[dat, Frame -> True, 
 FrameTicks -> {{PowerTicks[True], 
    PowerTicks[False]}, {PowerTicks[True], PowerTicks[False]}}]