Logan played alto and tenor saxophone, bass clarinet, flute, piano and oboe. He collaborated with Archie Shepp, Pharoah Sanders and Bill Dixon before forming his own quartet made up of pianist Don Pullen, bassist Eddie Gómez and percussionist Milford Graves.
Logan was a member of Byard Lancaster's band and toured with and appeared on records by Patty Waters. He recorded two albums for the ESP-Disk record label and later appeared on an album by Roswell Rudd on the Impulse!