You can log your data manually, and plot this via ListPlot3D. The axes can be removed, or you can use Ticks specification to insert the correct labels.
For example:
Ticks -> {{}, {Log[10^#], 10^#} & /@ Range[0, 5]}
This plot option specifies 1, 10, ... , 100000 on a plot of logged data. This approach limits dynamic labeling (as we've specified the range and interval), but should you find it necessary it could be worked on.
