Here is a simple .nod program with logarithmic spacing of between 2 and 20 points, on a line from x=1 to x=10. (Slider numbers can be altered.)
Also included are a few demo nodes, Flowing the points to another curve (a longer line in the demo), with Stretch option.

It is also possible to do Geometric spacing, in another node. (Progressive node has geometric progression.)

The fairly simple math equations came from a typewriter era program called Gridder (BSD license), and are explained in Appendix I of the Users Manual.
(There are numerous typo errors in Appendix I, but not too serious. It was fun and only a little awkward to understand and verify the equations, with a few corrections.)
(Source code was not examined.)

https://meshing.lanl.gov/gridder/users_manual.html
https://meshing.lanl.gov/gridder/gridder.html

- Brian