Definitions of log:

• noun:   measuring instrument that consists of a float that trails from a ship by a knotted line in order to measure the ship's speed through the water
• noun:   a written record of events on a voyage (of a ship or plane)
• noun:   a written record of messages sent or received

  Example: "They kept a log of all transmission by the radio station"

• noun:   a segment of the trunk of a tree when stripped of branches
• noun:   the exponent required to produce a given number
• noun:   large log at the back of a hearth fire
• verb:   enter into a log, as on ships and planes
• verb:   cut lumber, as in woods and forests