means A length of trunk or thick branch cut from a felled tree — or, by extension, a running record of events kept in sequence.

from From Old English or early Germanic stock, related to Old Norse 'lág' meaning a felled tree. The record-keeping sense sailed in later: ships measured speed by tossing overboard a 'log' — a wooden float on a knotted line — and noting the readings in the 'log-book.' So the dead tree got a second job as a tally of miles, and eventually any kept record became a 'log,' verb and all.