<< Graphics`Graphics`

tauNoverTauP1 = 
        1*((1/x)^(1/1) - 1)/
            Log[1/x];
tauNoverTauP2 = 
        2*((1/x)^(1/2) - 1)/
            Log[1/x];
tauNoverTauP3 = 
        3*((1/x)^(1/3) - 1)/
            Log[1/x];
tauNoverTauP4 = 
        4*((1/x)^(1/4) - 1)/
            Log[1/x];
tauNoverTauP6 = 
        6*((1/x)^(1/6) - 1)/
            Log[1/x];
tauNoverTauP10 = 
        10*((1/x)^(1/10) - 1)/
            Log[1/x];
LogLogPlot[{tauNoverTauP1, tauNoverTauP2, tauNoverTauP3, 
          tauNoverTauP4, tauNoverTauP6, tauNoverTauP10}, {x, 0.01, 0.4}, 
        PlotRange -> {1, 30}, 
        PlotStyle -> {Thickness[0.002], Thickness[0.002], 
            Thickness[0.002], Thickness[0.002], Thickness[0.002], 
            Thickness[0.002]}, 
        GridLines -> {{0.01, 0.011, 0.012, 0.013, 0.014, 0.015, 0.016, 
              0.017, 0.018, 0.019, 0.02, 0.021, 0.022, 0.023, 0.024, 0.025, 
              0.026, 0.027, 0.028, 0.029, 0.03, 0.031, 0.032, 0.033, 0.034, 
              0.035, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 
              0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 
              0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 
              0.33, 0.34, 0.35, 0.4}, {1, 2, 3, 4, 5, 10, 20, 
              30}}];