The tone equalizer is based on an early version of the one of @anon41087856 (see https://discuss.pixls.us/t/a-tone-equalizer-in-darktable), with some tweaks. Essentially it’s a parametric tone curve, but it operates in scene-referred space (meaning no clipping, unbounded data), and happens much earlier in the pipeline than the usual tone curves. It gives you a way of controlling the tonal balance of the image. I use it very often personally.
Log encoding is a way of mapping from scene-referred to display-referred, using the ACES formula that you can find at GitHub - ampas/aces-dev: AMPAS Academy Color Encoding System Developer Resources (and which has been discussed extensively here as well), plus a re-linearization afterwards. You can view it as a “poor man”'s filmic, covering only the basics, without the magic of the desaturation and tone curves, which in ART you have to do by hand with the curves in the tone curve tool (this is by design). You can view this as an alternative to the dynamic range compression tool if you want (though nothing prevents you from using both). Personally, I like the output of dynamic range compression better most of the time, but there are situations in which log encoding is useful and works pretty well.
For both tools, the “detail” slider tries to preserve the local contrast. If abused, it can introduce halos. If that happens, move the slider to the left until the halos go away (or find the sweet spot between artifacts and detail preservation…)
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