Rescale x-axis of an Histogram with fixed bins

Question

I produced an histogram using this simple code:

Histogram[{data}]

where data is a set of 100 values. The result was:

I now would like to "rescale" the x-asis in order to obtain something like this

I tried with Histogram[{data}, {{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048,4096}}] but it didn´t work because in the x-axis there are still all bins, not only the one I want.

Do you have any idea on how to solve my problem?

Answer 1

Obtain bar heights using HistogramList with your bin specification, and use the result in BarChart:

data = RandomVariate[WeibullDistribution[2, 5], 1000];
binspec = {Prepend[2^Range[0, 13], 0]};
xlabels = Rotate[Style[#, 16, "Panel"], Pi/2] & /@ Append[binspec[[1, 2 ;; -2]], Infinity];

heights1 = HistogramList[data, binspec, "Count"][[2]];
BarChart[heights1, ChartLabels -> xlabels, BarSpacing -> 0]

heights2 = HistogramList[data, binspec, "Probability"][[2]];
BarChart[heights2, ChartLabels -> xlabels, BarSpacing -> 0]