THE MANY DISTRS OF AN ACFT CHANGE AND A QUICK TURN AROUND RESULT IN A DEP WITH AN OPEN LOG ITEM.

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WE WERE RESCHEDULED TO FLY ACFT X AFTER OUR ACFT WENT DOWN WITH A MECHANICAL. ACFT X WAS COMING INBOUND. BY THE TIME THAT THE ACFT PULLED IN TO THE GATE WE WERE OVER AN HR LATE. THEN WE WERE HELD OFF OF THE ACFT WHILE THE INBOUND CREW CLRED CUSTOMS; SO I NEVER TALKED TO THE INBOUND CREW. THE ACFT SPENT OVER AN HR ON THE GATE; BUT WE WERE ONLY IN IT GETTING READY TO GO MAYBE 35-40 MINS OF THAT HR. ONCE WE WERE LET ONTO THE AIRPLANE; WE WERE TRYING TO MAKE UP TIME. I LOOKED IN THE LOGBOOK AND SAW THE INBOUND WRITE-UP FOR A TRAY TABLE NEEDING ADJUSTMENT; PUT MY SIGNATURE NEXT TO IT; AND THEN GOT INVOLVED GETTING THE AIRPLANE READY TO LEAVE; AND ENDED UP FORGETTING ABOUT THE WRITE-UP WHEN WE DID THE CHKLIST. I THINK THAT I SUBCONSCIOUSLY THOUGHT THAT SOME OF THE ACTIVITY BEHIND ME IN THE DOOR WAY TO THE COCKPIT WAS MAINT TAKING CARE OF THE BOOK. BUT MAINT NEVER SHOWED UP. LATER; I SURMISED THAT THE INBOUND CREW NEVER SENT A MESSAGE ABOUT THE WRITE-UP AND/OR CALLED MAINT ABOUT IT ONCE THEY PULLED ONTO THE GATE. MY FO NEVER CHKED THE LOGBOOK SO THAT LINE OF DEFENSE FELL APART. AND I'M SURE THAT THE FLT ATTENDANTS ON THE INBOUND CREW INFORMED THE COCKPIT ABOUT IT AFTER THEY WERE PARKED AT THE GATE. THE BOTTOM LINE IS THAT I LOOKED AT IT; SIGNED IT; AND FORGOT ABOUT IT BY THE TIME WE DID THE CHKLIST.