I have been toying the idea of Logan's Run as soon as I am done with The Descent of Anansi by Larry Niven.
Do you have the isbn of the book? Since it was also a movie are there two different version? I know sometimes an original gets published, then after the movie comes out - another version Based on the movie is published.
The original book (part of a 3 part planned trilogy IIRC that never got completed) is vaguely similar to the movie. But the death age was different, no domed city as they had the whole Earth to roam in. And (I may be conflating stories now) Logan was getting smuggled to Mars, which was where the 2nd book was to be placed.
Sort of like Planet of the Apes - the original book was entirely different than the movies (high tech Apes in Space! Studio figured they could not afford the effects so changed, well, pretty much everything)