I may have badly expressed myself.
This of course only makes sense with gPad->SetLogx() and no negative values in xbins[].
With a log-equidistant binning, the mean is :
0.5*(ln E1 + ln E2) i.e. sqrt(E1E2) in logx (e.g. sqrt(10^010^2) = 10).
Just a proposal…

We are not supporting log-equidistant histograms, that can be built directly, so we cannot implement this.
Adding this feature would also add quite some complexity to the histogram classes.
If you want to do that from the beginning, why not filling directly the histogram with log(x) ?

Just in case, attached’s a script to compute the mean, rms, mean error and rms error of a log-equidistant histogram and display the corresponding (corrected) statbox.