Ggtkuk

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] &, 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 -> ""]]

ListLinePlot + ScalingFunctions

ListLinePlot[data, BaseStyle -> Directive[AbsoluteThickness[36], CapForm["Butt"]], 
 ScalingFunctions -> "Log", "Linear", AspectRatio -> 1/2, 
 ImageSize -> Large, PlotRange -> 0, 6, Frame -> True, 
 FrameTicks -> None, None, 50, 100, 200, 500, 1000, Automatic, 
 Epilog -> MapIndexed[Text[Style[labels[[#2[[1]]]], White, 
 FontSize -> Scaled[.03]], #, #2[[1]], Center] &, Log[GeometricMean /@ dates]]]

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[Log@#, # &@50, 100, 200, 500], None]

BarChart

BarChart[Style[#[[1]], Directive[EdgeForm[], White]], 
 Labeled[Style[#[[2]], Directive[EdgeForm[], #2]], 
 Style[#3, White, FontSize -> Scaled[.03]], Center] & @@@ 
 Transpose[dates, ColorData[97] /@ Range[Length@dates], labels], 
 BarOrigin -> Left, BarSpacing -> 0, .25, ChartLayout -> "Stacked", 
 ScalingFunctions -> "Log", Axes -> False, 
 PerformanceGoal -> "Speed", Frame -> True, ImageSize -> Large, 
 PlotRangePadding -> .5, AspectRatio -> 1/2]

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]]

A = 10^5; B = 5;
rectangle[start_, length_, number_] := 
 RegionPlot[Log10[start] <= x <= Log10[start + length] && 
 number <= y <= number + .75, x, 0, Log10[A], y, 0, B, 
 PlotStyle -> LightBlue, BoundaryStyle -> Blue]; 
Show[
 rectangle[10, 300, 1], rectangle[100, 3000, 2], rectangle[1000, 30000, 3], 
 FrameTicks -> Transpose@Range[0,5], 10^Range[0,5], Automatic, None, None, 
 AspectRatio -> 1/2
]