The most common and most likely answer to this crossword clue is the 4 letter word EXIT
E
X
I
T
More clues leading to the result EXIT
- Cross character in formal attire getting up to go
- Go without nookie?
- Death of former partner with sex appeal
- Leave old computer equipment
- Sexy with no clothes? Leave!
- Departure times appearing on it after the introduction of electricity
- Leave cardinal in Rome, breaking heart of deity
- English team facing shoot-out ultimately making this?
- Leave 10 in drawback
- It may support a former spouse in retirement
Buddy explains!

The straight part
We know that "log-off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case log-off = exit.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EXIT mean?
EXIT noun- An act of going out or going away, or leaving; a departure.
- A way out.
- The act of departing from life; death.
- To go out or go away from a place or situation; to depart, to leave.
- To depart from life; to die.
- To end or terminate (a program, subroutine, etc.)
- (originally United States) To depart from or leave (a place or situation).