The logarithmic shadow mapping split scheme produces split points that minimize aliasing. There is a short derivation that can be used to show that it produces the split points that reduce aliasing to values near 1. Here is the calculation:
$C^{log}_i = z_n(\frac{z_f}{z_n})^\frac{i}{m}$
where $i$ is the ith cascade and m is the total number of cascades.
Chose $z_n$ carefully. Often it is better to use a "virtual" near plane chosen to maximize coverage and reduce wasted shadow map space. (A poorly chosen near plane can cause an entire cascade to produce no meaningful data) Also, keep in mind that shadows closer to the camera then the chosen near plane will still produce shadows but may have higher aliasing. There are algorithms for choosing a virtual near plane I recommend looking them up.
While $C^{log}_i$ will produce split points that minimize aliasing, it will generally not give the best coverage for distant shadows(where the majority of the geometry is rendered). And a better scheme (published in several places) is to use something called the "practical" or "weighted" algorithm. It combines a uniform distribution with the logarithmic distribution. Here is its calculation: (just a simple lerp)
$C^{pract}_i = \alpha C^{log}_i + (1-\alpha)C^{uni}_i$
where $C^{uni}_i$ is:
$C^{uni}_i= n + (f-n)\frac{i}{m}$
This makes it easy to adjust between full logarithmic and uniform split.
Most of this info is readily available but the bit about choosing Z near is glossed over in most publications.
Here are my sources:
My used copy of "Real-Time Shadows" and GPU Gems 3 chapter 10 (because there was an error in the book!)
