plotting - Using Show to place a ParametricPlot on a LogLog scale

I wish to have a few plots on the same graph: ListLogLogPlot, LogLogPlot and a ParametricPlot drawing lines perpendicular to the x-axis. The problem is however that ParametricPlot doesn't seem to have the LogLog equivalent, as the other Plot functions do, and Show does not combine non-LogLog plots with LogLog plots, even when they coincide, eg.:

Show[LogLogPlot[x^4, {x,10^(-10),10^10}], Plot[x^5, {x,10^(-10),10^10}]]

should theoretically show two straight lines, but shows only one. Is there a way to combine such graphics without resolving to using non-LogLog plots?

Answer

Try this:

    Show[{
  LogLogPlot[x^4, {x, 10^(-10), 10^10}, PlotStyle -> Red], 
  LogLogPlot[x^5, {x, 10^(-10), 10^10}, PlotStyle -> Blue],
  ParametricPlot[{Log[0.01], Log[y]}, {y, 10^-26, 10^30}, 
   PlotStyle -> Darker@Green]
  }]

enter image description here

Comments

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plotting - Plot 4D data with color as 4th dimension

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plotting - Mathematica: 3D plot based on combined 2D graphs

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