logarithm vs log

logarithm and log both are nouns.

Word	Noun	Adjective	Verb	Adverb
logarithm	Yes	No	No	No
log	Yes	No	Yes	No

As nouns, logarithm and log are synonyms defined as:

logarithm (noun)	log (noun)
the exponent required to produce a given number	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
	a written record of events on a voyage (of a ship or plane)
	the exponent required to produce a given number
	a written record of messages sent or received
	a segment of the trunk of a tree when stripped of branches

logarithm (verb)	log (verb)
	enter into a log, as on ships and planes
	cut lumber, as in woods and forests