‹›Visualization: Labels, Scales, ExclusionsScale Any Axes
Apply scaling functions to any axis.
show complete Wolfram Language input
options = 
  Sequence @@ {ImageSize -> 250, 
    PlotRange -> {{0.5, 1.5}, {0.1, 2}}};
Grid[Partition[{
   Plot[{x^(1/4), x^(3/4), x^(3/2), x^(7/2)}, {x, 0, 2}, 
    Evaluate@options, PlotLabel -> "Linear, Linear"],
   Plot[{x^(1/4), x^(3/4), x^(3/2), x^(7/2)}, {x, 0, 2}, 
    Evaluate@options, PlotLabel -> "Linear, Log", 
    ScalingFunctions -> "Log"],
   Plot[{x^(1/4), x^(3/4), x^(3/2), x^(7/2)}, {x, 0, 2}, 
    Evaluate@options, PlotLabel -> "Log, Linear", 
    ScalingFunctions -> {"Log", "Linear"}],
   Plot[{x^(1/4), x^(3/4), x^(3/2), x^(7/2)}, {x, 0, 2}, 
    Evaluate@options, PlotLabel -> "Log, Log", 
    ScalingFunctions -> {"Log", "Log"}]}, 2]]