What was found
ECAM, SMOKE LAVATORY DET FAULT, POSTED WHILE TAXING OUT FOR TAKEOFF. FLIGHT ATTENDANTS REPORTED SMELLING BURNING SMELL FROM AFT RIGHT LAV. PERFORMED LAV A SMOKE DETECTOR TEST IAW 26-17-15, TESTED OK. NO DEFECTS NOTED IAW AMM 26-17-00-710-001-A. TROUBLE SHOT IAW TSM 71-00-00-810-802-A & 05-50-00-810-831-A. INSPECTED AFT LAVS LIGHTING, ASSOCIATED LAV SYS & WIRING, INSPECTED AFT GALLEY AREA, WIRING & LIGHTING ALL WITH NO FINDINGS OR ABNORMAL SMELLS NOTED. LAV OPERATIONS CHECKED NORMAL. PERFORMED ENG RUNS & OPERATED PACKS, COULD NOT DUPLICATE REPORTED BURNING SMELL. SHUTDOWN & RESTARTED ENGS. NOTICED SLIGHT ENG EXHAUST SMELL IN AFT CABIN WITH PACKS OFF, DOORS CLOSED & OUTFLOW VLV OPEN. CONTACTED TECH SUPPORT. TECH SUPPORT NOTIFIED VIA M508. IAW REVIEW OF M508 & MX ACTIONS PERFORMED, ACCOMPANIED BY NO HISTORY OF BURNING SMELL IN THE CABIN, ADVISED TO CONTINUE ACFT REVENUE SERVICE WITHOUT ANY FURTHER MX ACTION AT THIS TIME. ACFT OK FOR SERVICE.