Plotting curves in 3D with different scales on different axes

Question

I want to plot 1D functions in 3D using LogLog scale. So suppose I have 1D equation for a function like $y=x^2$ and I want to label it by an additional number $z=1$. The second function could be $y=x^2+1$ labeled by $z=2$. I want those $y=f(x)$ curves to be 1 dimensional, not surfaces and plotted in LogLog scale, and labeling given by $z$ to be given in linear scale. Plots should be just curves on $x,y$ plane labeled on the third axis $z$. How can I do that?

  a = Plot3D[{{y = x^2}, {z = 1}}, {x, 0, 10}, {z, 0, 10}]
  b = Plot3D[{{y = x^3}, {z = 2}}, {x, 0, 10}, {z, 0, 10}]
  Show[a, b] 

This is what I tried. It gives me a surface not a curve and doesn't work at all.

Answer 1

func = Table[{x, i, x^(i + 1)}, {i, 5}]

ParametricPlot3D[Evaluate @ func, {x, 0, 10}, 
 AxesLabel -> {"x", "z", "y"}, 
 ScalingFunctions -> {"Log10", Identity, "Log10"},
 BoxRatios -> {1, 1, 1},
 ViewPoint -> {0, -2, 0}]

Without ViewPoint:

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• More on ScalingFunctions in this thread.