Allow two to three weeks for a good event logo with two feedback rounds.
Week 1: brief and first sketches, usually three to five directions.
Week 2: choice of direction, refinement and feedback round.
Week 3: refinement and delivery in all file formats.
Faster is possible, but not without trade-offs. A logo you get within three days is almost always the first thing the designer came up with. And that is rarely the best.
Start at least three weeks before you want to send the save-the-date. Four to five weeks is more comfortable.