I took a look at the histogram; in my program, it looks almost flat. I tried changing the contrast; nothing really looked good and nothing that I did really did anything for that white log.
I've made some alterations to the image, toning down the log to bring out some more detail (all done in Lightroom).
Incidentally, I suspect you have some misunderstandings as regards histograms. A flat histogram merely indicates that over the whole of the image, there's an even distribution of tones. It has nothing whatever to do with contrast. If you take a shot of a mid-gray card, you'll see a histogram with a single peak in the midtones and nothing (much) elsewhere, but it will still be a flat image, lacking in any contrast. The reverse is true as well.