keep one's nose to the grindstone vs slog

keep one's nose to the grindstone and slog both are verbs.

Word	Noun	Adjective	Verb	Adverb
keep one's nose to the grindstone	No	No	Yes	No
slog	No	No	Yes	No

As verbs, keep one's nose to the grindstone and slog are synonyms defined as:

keep one's nose to the grindstone and slog: work doggedly or persistently

Other synonyms of keep one's nose to the grindstone include keep one's shoulder to the wheel, peg away, plug away.

keep one's nose to the grindstone (verb)	slog (verb)
work doggedly or persistently	strike heavily, especially with the fist or a bat
	walk heavily and firmly, as when weary, or through mud
	work doggedly or persistently