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We have data series:

data1={{0., 5.02512*10^-10}, {0.06668, 2.99284*10^-8}, {0.13336,
 3.22116*10^-8}, {0.20004, 2.58191*10^-8}, {0.26672,
 1.99125*10^-7}, {0.3334, 1.21646*10^-8}, {0.40008,
3.35916*10^-7}, {0.46676, 3.79768*10^-7}, {0.53344,
1.02102*10^-7}, {0.60012, 1.17535*10^-6}, {0.6668,
 1.72507*10^-7}, {0.73348, 1.23789*10^-6}, {0.80016,
 1.9808*10^-6}, {0.86684, 1.39616*10^-7}, {0.93352,
 4.60649*10^-6}, {1.0002, 1.39262*10^-6}, {1.06688,
 3.83127*10^-6}, {1.13356, 0.0000101002}, {1.20024,
 3.26005*10^-8}, {1.26692, 0.0000229263}, {1.3336,
0.0000144712}, {1.40028, 0.000020778}, {1.46696,
 0.000134013}, {1.53364, 4.94753*10^-6}, {1.60032,
 0.00250851}, {1.667, 0.00326501}, {1.73368, 0.0000968109}, {1.80036,
  0.000207831}, {1.86704, 7.79724*10^-6}, {1.93372,
  0.0000459028}, {2.0004, 0.0000321442}, {2.06708,
  2.43685*10^-6}, {2.13376, 0.0000276559}, {2.20044,
   3.87948*10^-6}, {2.26712, 9.62673*10^-6}, {2.3338,
  0.0000130072}, {2.40048, 1.53889*10^-7}, {2.46716,
  0.0000116171}, {2.53384, 3.36691*10^-6}, {2.60052,
  3.53838*10^-6}, {2.6672, 8.3132*10^-6}, {2.73388,
   2.36251*10^-8}, {2.80056, 6.58432*10^-6}, {2.86724,
  3.33096*10^-6}, {2.93392, 1.45936*10^-6}, {3.0006,
   6.35157*10^-6}, {3.06728, 2.69642*10^-7}, {3.13396,
  4.25243*10^-6}, {3.20064, 3.49319*10^-6}, {3.26732,
 5.50908*10^-7}, {3.334, 5.33684*10^-6}, {3.40068,
   6.86369*10^-7}, {3.46736, 2.92315*10^-6}, {3.53404,
    3.88476*10^-6}, {3.60072, 1.32685*10^-7}, {3.6674,
   4.88858*10^-6}, {3.73408, 1.2985*10^-6}, {3.80076,
   2.10915*10^-6}, {3.86744, 4.63201*10^-6}, {3.93412,
   9.45702*10^-10}, {4.0008, 4.94888*10^-6}, {4.06748,
   2.37468*10^-6}, {4.13416, 1.60386*10^-6}, {4.20084,
  6.40728*10^-6}, {4.26752, 1.82055*10^-7}, {4.3342,
  6.14228*10^-6}, {4.40088, 5.175*10^-6}, {4.46756,
   1.4092*10^-6}, {4.53424, 0.000013092}};

And we wish to have bellow command which drives us crazy:

ListLogPlot[{data1},
       Epilog -> {
     Style[Text["a", {2, 10^-6}], 11, Bold, Background -> White],
     Style[Text["b", {2, 10^-7}], 11, Bold, Background -> White],
     Style[Text["c", {2, 10^-9}], 11, Bold, Background -> White],
     Style[Text["d", {2, 10^-11}], 11, Bold, Background -> White]}
      ]
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  • 1
    $\begingroup$ You can try with ListLogPlot[{data1}, Epilog -> {Style[Text["a", {2, 10^-6}], 11, Bold, Background -> White], Style[Text["b", {2, 10^-7}], 11, Bold, Background -> White], Style[Text["c", {2, 10^-9}], 11, Bold, Background -> White], Style[Text["d", {2, 10^-11}], 11, Bold, Background -> White]} /. {x_?NumericQ, y_?NumericQ} -> {Log[x], Log[y]}]. $\endgroup$ – b.gates.you.know.what Dec 27 '15 at 15:36
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The Epilog option is not used by ListLogPlot directly. It is simply passed on to the Graphics expression returned by ListLogPlot. The coordinates you use in Epilog are interpreted in the standard coordinate system, not in a special logarithmic one. Thus you must transform your coodrinates manually.

Instead of {2, 10^-7} use {2, Log[10^-7]}.

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ListLogPlot[data1,
 Epilog -> 
  MapThread[Style[Text[#1, {##2}], 11, Bold, Background -> White] &,
   {{"a", "b", "c", "d"}, {2, 2, 2, 2}, Log[10 ^-{6, 7, 9, 11}]}],
 GridLines -> Automatic,
 PlotRange -> {Automatic, {10^-12, Automatic}}]

enter image description here

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