# How can I change the scale in two particular ranges of values in a graphic?

The graphic of this function is very condensed between $0\leq n\leq 500$. But it is more expansive among $500\leq n\leq 5000$.

How can I change the scale in two particular ranges of values in a graphic?

ListPlot[Table[Sin[50/n^2], {n, 1, 50, 0.01}]]


You can try:

ListLogLinearPlot[Table[Sin[50/n^2], {n, 1, 50, 0.01}]]


ListPlot[Table[Sin[50/n^2], {n, 1, 50, 0.01}],
ScalingFunctions -> {"Log"}]


ListPlot[
Table[Sin[50/n^2], {n, 1, 50, 0.01}],
Epilog -> Inset[ListPlot[
Table[Sin[50/n^2], {n, 0.01, 1, 0.001}],
Joined -> True, PlotStyle -> Red], {2800, .5}]
]


Of course you can place the Inset wherever you like by changing the coordinates.

Adjust the parameters as you like in the following:

ListPlot[
Table[{n, Sin[50/n^2]}, {n, 1, 50, 0.01}],
Epilog -> Inset[ListPlot[
Table[{n, Sin[50/n^2]}, {n, 0.01, 1, 0.001}],
Joined -> True, PlotStyle -> Red, AspectRatio -> 3,
ImageSize -> 100], {30, 0.5}],
ImageSize -> 500
]