I want to recreate a ListLogLinearPlot with a point at 0 and at infinity. I wish to recreate a logarithmic x-axis that extends to zero and infinity, as seen in the picture below:

Example of an "extending" x-axis to both zero and infinity.

How would I go about extending the axis like so? And given this axis, would Mathematica recognize where to put a point with coordinates {0,#} or {\[Infinity],#}?

A "cheated" graph, where only the labels are replaced but the true values are finite, would also be acceptable. Still, how would I make the nice squiggly line that indicates the infinite extension of the axis?