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I'm trying to draw a vertical line on a LogPlot using Epilog. There is a slight issue in the vertical positioning of the line. When I indicate the line should begin at 1 it instead begins at ~2.75.

LogPlot[Exp[x], {x, 0, 3}, Epilog -> Style[Line[{{2, 1}, {2, 10000}}], Thickness[.005]]]

Attempting to extend the line by lowering the starting point was unsuccessful. Raising the line works, but the starting point still doesn't correspond exactly to that requested. The issue is absent when doing a Plot command and present when doing other variants of Plot where the axis are on a Log scale.

enter image description here

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LogPlot[Exp[x], {x, 0, 3}, 
 Epilog -> Style[Line[{{2, Log@1}, {2, 10000}}], Thickness[.005]]]

enter image description here

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