Logan studied at Culver Military Academy and at Princeton University, which was where he became interested in drama. In the 20s he established a Cape Cod summer stock troupe, the University Players. He was awarded a scholarship to study with Constantin Stanislavsky in Moscow, Russia and after his return in 1932 worked in Hollywood as dialogue coach on The Garden Of Allah (1936) and History Is Made At Night (1937); he also co-directed with Arthur Ripley I Met My Love Again (1938). He also directed plays on Broadway, among them On Borrowed Time, I Married An Angel, Knickerbocker Holiday (all 1938) and By Jupiter (1940). Logan then collapsed with exhaustion and entered a psychiatric hospital as a voluntary patient. Upon his return to work, he found great success on Broadway with four musicals, all of which were huge hits. These were Irving Berlin’s Annie Get Your Gun (1946), Richard Rodgers and Oscar Hammerstein II’s South Pacific (1949), of which he was also co-writer of the libretto, Wish You Were Here (1952) and Fanny (1954), also co-librettist, and he also worked on 1962’s All American, Mel Brooks’ first musical. He also directed several non-musicals, among them Mister Roberts (1948), which he co-wrote, The Wisteria Trees (1950), Picnic (1953) andMiddle Of The Night (1956). Another period of psychiatric illness followed before Logan began a sustained period of work in Hollywood. His films enjoyed less acclaim than his stage work, even when he directed screen versions of his stage shows. Among films from this period are Picnic (1955), Bus Stop (1956), Sayonara (1957), South Pacific (1958) and Fanny (1961).

During the 60s, Logan was again troubled with poor health but by the end of the decade was successfully treating his depression with lithium carbonate and subsequently became an active proponent of changing attitudes inside and outside the medical profession for treatment of mental illness. Throughout the 60s and succeeding decades Logan remained active in films and the theatre, but had no real successes in either medium. The stage shows included Mr. President (1962), Look To The Lillies (1970), Miss Moffat (1974) and Horowitz And Mrs. Washington (1980). Among his late films are Camelot (1967) and Paint Your Wagon (1969). At the time of his death, he was working on a new musical based on Mark Twain’s Huckleberry Finn.