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I was trying to plot a vertical line using ListPlot everything works perfectly:

MassPeaks = {{9.1, 0}, {9.1, 2}};
ListPlot[MassPeaks, Joined -> True]

However, if I change ListPlot to ListLogPlot my line disappears:

ListLogPlot[MassPeaks, Joined -> True]

shows the same axes but no line. Is this a bug or I am missing something?

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Since Log[0] evaluates to Infinity you need a value close to 0. You also should specify PlotRange to get a "nice" scaling.

ListLogPlot[{{9.1, 2}, {9.1, 0.00001}},
 Joined -> True,
 PlotRange -> {Automatic, {0.1, 4}}]

enter image description here

Another possibility:

ListLogPlot[{{9.1, 2}}, Filling -> Bottom]

enter image description here

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