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 The O.C. (2003) and 24 (2001). His breakthrough role came in Ridley Scott's Prometheus (2012).