A fatigued A319 Flight Crew reported encountering wake vortex on approach to LAX; causing enough distraction that the gear was not extended until they got the warning.

Narrative

Creeping fatigue had a definite effect to cause me to not put the gear down in a timely manner. We were following a B747 on a visual approach by 4.5 miles. We encountered wake turbulence at about the time we usually put the gear down. We encountered it again at 1000 feet one dot above the glide slope and I remembered being annoyed that the B747 was high on glide slope. We missed the 1000 foot call. At 700 feet the gear warning bell sounded and we put the gear down before 500 feet. I remember thinking that as tired as we both were it would be safer to land than to go around beating ourselves up going around the pattern. I knew we had gear and full flaps so I used my emergency authority and landed. We had flown a tough three day trip were fatigue crept up on us. I felt OK [on departure]; however; I felt very tired at the top of descent. We had a very short night the night before. I believe that it was a chain of events that led to our not getting the gear down in a timely manner. Fortunately; the system worked and we landed safely.