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LUT's are Lookup tables, it is a tiny file that a camera manufacturer provides to preview the LOL video in the correct colors. Usually a .cube file "V-Log-Rec709.cube" indicates a Panasonic V-LOG to standard screen preview.
The is no processing or conversion involved.
LOG files and any video files recorded in a flat profile LOG. This is used to maximize the exposure and contrast of video for post-production.
iPhone to Canon, Panasonic, Nikon,Red, Arri, make video clips this way. they would be called AppleLog, C-Log, V-Log, N-Log and so on.
a pulldown menu would allow you to select the .cube file and preview a video file in the correct colors it was recorded. instead of seeing a grey flat image.
i am including a screenshot of the different views.
i can make a screen recording if this helps.