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I have this code but I don't know how can I put the y-axis in a logarithmic form (I need to put it in a base 2 logarithm and in the default Log of mathematica), because there is an incompatibility between LogPlot and ListLogPlot with the option ScalingFunction "Reverse". I hope you can help me. The code is the following:

data1 = {{0.18170805572380375`,10.66}, {0.18170805572380375`,10.6925}, {0.18170805572380375`,10.725}, {0.18170805572380375`,10.7575}, {0.18170805572380375`,10.79}, {0.18170805572380375`,10.8225}, {0.18170805572380375`,10.855}, {0.18170805572380375`,10.8875}, {0.17947950942267424`,11.2125}, {0.17947950942267424`,11.5375}, {0.17947950942267424`,11.83}, {0.17730496453900707`,12.1875}, {0.17730496453900707`,12.51255}, {0.17730496453900707`,12.7075}, {0.17730496453900707`, 12.8375}, {0.1751824817518248`, 13.065}, {0.1751824817518248`, 13.4875}, {0.1751824817518248`, 13.8125}, {0.1751824817518248`, 14.1375}, {0.17311021350259664`,14.4625}, {0.17311021350259664`, 14.7875}, {0.17108639863130878`,16.0875}, {0.1691093573844419`, 18.6875}, {0.1691093573844419`,21.9375}, {0.16717748676511562`, 25.1875}, {0.16717748676511562`,27.4625}, {0.16717748676511562`, 29.0875}, {0.16528925619834708`,30.0625}, {0.16528925619834708`, 31.3625}, {0.16528925619834708`,33.9625}, {0.16528925619834708`, 36.5625}};
data2 = {{0.11846001974333663`, 10.66}, {0.11657276083155237`,10.6925}, {0.11565150346954509` , 10.725}, {0.11385199240986715`,10.7575}, {0.1129730747505178`, 10.79}, {0.11125533098460968`,10.8225}, {0.11041589988958408`, 10.855}, {0.10877447425670773`,10.8875}, {0.10055304172951232`, 11.2125}, { 0.09408812921436412`,11.5375}, {0.08894159501927067`, 11.83}, {0.08432888264230498`,12.1875}, {0.08017103153393906`, 12.5125}, {0.07845188284518828`,12.7075}, {0.07680491551459293`, 12.8375}, {0.07484096295372333`,13.065}, {0.07119971520113919`, 13.4875}, { 0.06853226727584237`,13.8125}, {0.06635700066357`, 14.1375}, {0.06403415154749198`,14.4625},{0.06213109661385523`,14.7875}, {0.055319933616079654`, 16.0875}, {0.04537205081669691`,18.6875}, {0.037091988130563795`,21.9375}, {0.03143500812071043`, 25.1875}, {0.028386242134645405`,27.4625}, {0.026581605528973946`,29.0875}, {0.025560194257476354`,30.0625}, {0.024368450978799448`, 31.3625}, {0.02225601839830854`,33.9625}};
Show[Plot[7.672566821271195` + 0.19053345681644884`/t^1.3`, {t, 0, 0.18251}, PlotRange -> {{0, 0.2}, {0, 50}}, AxesOrigin -> {0, 50},ScalingFunctions -> "Reverse", AxesStyle -> {Directive[Black, Thick], Directive[Black, Thick]},  TicksStyle -> {{FontSize -> 20, Black}, {FontSize -> 20, Black}}, LabelStyle -> {Directive[22, "Times", Red, Bold]},PlotStyle -> {Blue,Thickness[.008]},AxesLabel -> {Style[Text["  \!\(\*SuperscriptBox[\(\[Beta]\), \(-1\)]\) "], FontSize -> 26, Bold, Black],Style[Text["  L "], FontSize -> 26, Italic, Bold, Black]}, PlotRange ->{{0, 0.20}, {0, 50}}],Plot[-2.381937082936315` Tan[9.946572527751202486`3. t], {t, 0,0.18251}, PlotRange -> {0, 50}, AxesOrigin -> {0, 50},ScalingFunctions -> "Reverse",AxesStyle -> {Directive[Black, Thick], Directive[Black, Thick]},TicksStyle -> {{FontSize -> 20, Black}, {FontSize -> 20, Black}},LabelStyle -> {Directive[22, "Times", Red, Bold]}, PlotStyle -> {Red,Thickness[.008]},AxesLabel -> {Style[Text["  \!\(\*SuperscriptBox[\(\[Beta]\), \(-1\)]\) "],FontSize -> 26, Bold, Black],Style[Text[" L"], FontSize -> 26, Italic, Bold, Black]},PlotRange -> {{0, 0.20}, {0, 50}}],ListPlot[{data1, data2},PlotStyle -> {{Black,PointSize[0.010]},{Black, PointSize[0.012]}},AxesStyle -> {Directive[Black, Thick], Directive[Black, Thick]},TicksStyle -> {{FontSize -> 20, Black}, {FontSize ->20, Black}},AxesLabel -> {Style[Text["\!\(\*SuperscriptBox[\(\[Beta]\), \(-1\)]\) "],FontSize -> 26, Bold, Black],Style[Text[" L"], FontSize -> 26, Italic, Bold, Black]},PlotRange -> {{0, 0.20}, {0, 50}}, AxesOrigin -> {0, 50},ScalingFunctions -> "Reverse"]]
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Show[
  Plot[Log2[7.672566821271195 + 0.19053345681644884/t^1.3], {t, 0, 0.18251},
     ScalingFunctions -> "Reverse",
     PlotRange -> {{0, 0.2}, Log2@{1, 50}},
     AxesOrigin -> {0, Log2@50},
     AxesStyle -> {Directive[Black, Thick], Directive[Black, Thick]},
     TicksStyle -> {{FontSize -> 20, Black}, {FontSize -> 20, Black}},
     Ticks -> {Automatic, Thread[{Log2@#, #}] &[Round[2^Range[#, #2, (#2 - #)/6]]] &},
     LabelStyle -> {Directive[22, "Times", Red, Bold]},
     PlotStyle -> {Blue, Thickness[.008]},
     AxesLabel -> {Style[Text["  \!\(\*SuperscriptBox[\(\[Beta]\), \(-1\)]\) "], FontSize -> 26, Bold, Black], Style[Text["  L "], FontSize -> 26, Italic, Bold, Black]}], 
  Plot[Log2[-2.381937082936315 Tan[9.946572527751202486`3. t]], {t, 0, 0.18251},
     ScalingFunctions -> "Reverse",
     PlotStyle -> {Red, Thickness[.008]},
     PlotRange -> {{0, 0.20}, Log2@{1, 50}}],
  ListPlot[MapAt[Log2, {data1, data2}, {All, All, 2}],
     ScalingFunctions -> "Reverse",
     PlotStyle -> {{Black, PointSize[0.010]}, {Black, PointSize[0.012]}},
     PlotRange -> {{0, 0.20}, Log2@{1, 50}}]]
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  • $\begingroup$ Thank you Coolwater $\endgroup$ – Michaels Jul 18 '17 at 16:13
  • $\begingroup$ In the code above, to put it in the default Log of Mathematica is it sufficient to erase the 2 behind the Log2? $\endgroup$ – Michaels Jul 18 '17 at 16:23
  • $\begingroup$ You also need to change &[Round[2^Range to &[Round[E^Range $\endgroup$ – Coolwater Jul 18 '17 at 16:45
  • $\begingroup$ Ok, Thank you Coolwater $\endgroup$ – Michaels Jul 18 '17 at 16:57

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