Log Log scaling for the DensityPlot [closed]

Question

Consider some function f[x,y] where 10^-5 < x < 1 and 10^-8 < y < 10^6. As for example,

f[x_,y_]=Exp[-10^5. x^5 y]x^6

I want to make a density plot in the logarithmic scale (similar to LogLogPlot). The simplest option is to make

DensityPlotp[f[10^x,10^y],{x,-5,0},{y,-8,6}]

However, in this case, axes will show log[x], log[y] instead of x,y.

Could you please tell me how to make this thing properly?

Answer 1

As Michael noted, you can use ScalingFunctions, for both x and y axes.

DensityPlot[f[x, y], {x, 10^-5, 1}, {y, 10^-8, 10^6}, 
    ScalingFunctions -> {"Log", "Log"}, PlotRange -> All, 
    PlotLegends -> Automatic]

Most of the values are near zero, so you'll need to use PlotRange to see the full range of values. PlotLegends shows the range.