Yhyjyk

I need to plot something that looks like a gant chart, but are actual data ranges. These ranges need to be on a log scale. Graphics does not offer a Scalingfunction. A LogPlot with ErrorBars does not work either and would not look ideal. Is it possible to draw rectangles with one axis being log scale?

E.g.:
Min and Max values of the rectangles are the known data.

SeedRandom[1]
dates = Sort /@ RandomInteger[10, 1000, 5, 2];
data = MapIndexed[Thread@#, #2[[1]] &, dates];
labels = CharacterRange["A", "E"];
data2 = MapIndexed[Labeled[#, #2[[1]], Style[labels[[#2[[1]]]], White,
 FontSize -> Scaled[.03]], Center] &, N[GeometricMean /@ dates]];

ListLogLinearPlot

Show[ListLogLinearPlot[data, 
 BaseStyle -> Directive[AbsoluteThickness[36], CapForm["Butt"]], 
 Joined -> True, AspectRatio -> 1/2, ImageSize -> Large, 
 PlotRange -> 0, 6, Frame -> True, 
 FrameTicks -> None, None, 50, 100, 200, 500, 1000, Automatic],
 ListLogLinearPlot[data2, PlotMarkers -> ""]]

TimeLinePlot

TimelinePlot[Labeled[#, Style[#2, White, FontSize -> Scaled[.03]], Center] & @@@ 
 Transpose[Interval /@ (Map[N@*Log, dates, -1]), labels], 
 PlotStyle -> Directive[AbsoluteThickness[40], CapForm["Butt"]], 
 Spacings -> .1, PlotMarkers -> "", Frame -> True, 
 AspectRatio -> 1/2, PerformanceGoal -> "Speed", 
 FrameTicks -> Automatic, Automatic, 
 Transpose[N@Log@#, # &@50, 100, 200, 500], None]

Thanks: @David G. Stork for the GeometricMean idea to center the labels.

See also: Poets of the 19th century

LogLinearPlot[1, 
 t, .1, 100,
 PlotStyle -> White,
 Epilog -> Rectangle[Log[1], .5, Log[50], 1],
 Red, Rectangle[Log[30], 1.5, Log[80], 2],
 Text[Style["a", White, 18], Log[7], .75],
 Text[Style["b", White, 18], Log[53], 1.75]]

Here is a start ...

A = 10^5; B = 10; 
rectangle[start_, length_, number_] := RegionPlot[Log10[start] <= x <= Log10[start + length] && number <= y <= number + .75, x, 0, Log10[A], y, 0, B];

Then we place a few rectangle[]'s in Show[].

Show[rectangle[100, 300, 2], rectangle[200, 2000, 3], rectangle[1300, 3000, 4], rectangle[1800, 9000, 5]]

We now need to change the tick-marks and x-axis labels. I wanted to use ScalingFunction->"Log10",Automatic but this is not a valid argument for RegionPlot[].

Here is how it looks right now:

With your edits, we can get the x-axis looking better! Currently the x-axis label is $log_10 x $ and not $x$ as we would like.