I have a problem with the custom scaling of the axes for plots. I need a custom scaling function for both axes but I have found that even a basic example seems not to work as I intend to. Why the next two commands do not produce the same graph? It seems that the function g do not do anything and the function f transforms only y axis.
Plot[{Exp[x]}, {x, 0, 10}, ScalingFunctions -> {"Log", "Log"}, PlotRange -> All]
f[x_] := Log[x]
g[x_] := Log[x]
Plot[{Exp[x]}, {x, 0, 10}, ScalingFunctions -> {f, g}, PlotRange -> All]