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1. To count or record some number or amount of something. My fitness tracker logs up every step I take throughout the day to let me know how active I've been.
2. To acquire or accumulate a large number or amount of something, especially that which is added to a record or counter of some kind. If I have the right playlist of music playing, I can log up a lot of miles on my runs without even really feeling it in my legs.
log something up
to record an amount of something. The ship logged many nautical miles up on its last voyage. It logged up a lot of miles.