Etymology
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slog (v.)

1824, "hit hard," probably a variant of slug (v.3) "to strike." Sense of "walk doggedly" first recorded 1872. Related: Slogged; slogger; slogging.

slog (n.)

1846, "a hard hit," from slog (v.). Sense of "spell of hard work" is from 1888.

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Definitions of slog

slog (v.)
work doggedly or persistently;
Synonyms: plug away / peg away / keep one's nose to the grindstone / keep one's shoulder to the wheel
slog (v.)
walk heavily and firmly, as when weary, or through mud;
Synonyms: footslog / plod / trudge / pad / tramp
slog (v.)
strike heavily, especially with the fist or a bat;
Synonyms: slug / swig
From wordnet.princeton.edu