From Longman Dictionary of Contemporary Englishslog it outslog it out informalBritish EnglishFIGHTARGUE to fight, compete, or argue about something until one side wins The teams will be slogging it out on Saturday. → slog
Examples from the Corpus
slog it out• The answer is that you would have to slog it out all the way from London to Baghdad.• Byron was my hero and they've been slogging it out ever since. 