Making Axes logarithmic in 3d plots

Question

I've been trying to get loglog plots in 3D, but to no avail. My initial approach was to take the logarithm inside the plot i.e

Plot3D[Log[10,function[a, b]],{a, 1, 100000},{b, 1, 1000000}]

but now I'm looking for a way to logarithm-ise the axes as well. Any help would be greatly appreciated!

Answer 1

You first have to install the LevelScheme package, it's worth it if you produce a lot of figures.

Load the package:

<< LevelScheme`

Assign a function and do the 3D plot:

function = Log[10, a x + b /. a -> 1];
Plot3D[function, {x, 1, 3}, {b, -1, 3}, 
 PlotRange -> {{1, 3}, {-1, 3}, {-1, 1}}, 
 Ticks -> {LogTicks[10, 1, 3], LogTicks[10, -1, 3], LogTicks[10, -1, 1]}
]

This would produce this figure:

LevelScheme (and more specifically the Custom Ticks package) is really nice to do these things!

Answer 2

LogTicks is really nice. However, if you might wish to avoid another package or have more control over the final output, here is a template. As mentioned in a comment above, I actually hope that ScalingFunctions will be fully implemented in the future.

function[a_, b_] := Log[10, a + b]

Plot3D[Log[10, function[#^10 &@a, #^10 &@b]], {a, Log10@1, 
  Log10@100000}, {b, Log10@1, Log10@100000}, 
 Ticks -> {Table[{y, ToString[Round[10^y, 0.001]]}, {y, Log[10, 1], 
     Log[10, 100000]}], 
   Table[{y, 
     ToString[
      Round[10^y, 0.001] // ScientificForm // TraditionalForm]}, {y, 
     Log[10, 0.001], Log[10, 100000]}], Automatic}]