Logan is a native of Charleston, South Carolina. His parents are both drama teachers. His mother, Lowry Marshall, is the artistic director of Brown University's repertory theatre department.
Logan graduated with a Master's in Fine Arts from New York University's Graduate Acting Program at the Tisch School of the Arts.
He made a few appearances in Law and Order, before landing recurring roles on O.C., California (2003) and 24: Twenty Four (2001). His breakthrough role came in Ridley Scott's Prometheus - Dunkle Zeichen (2012).