Doesn't look like an audiobook of Logan's Run exists.
I have this book in my collection...
It includes all three of William F. Nolan's "Logan's" novellas: Logan's Run, Logan's World, and Logan's Search. It's a trade paperback, which is taller than a mass market paperback. And... Wow! I see it's out of print and selling for nearly $50 for a "Very Good" used copy. (Mine is "Like New".) That's ridiculous.