The Chicago White Sox selected Logan in the 20th round of the 2002 Major League Baseball draft. He advanced from the Sox's Rookie League affiliate, the Great Falls White Sox, straight to the major league club during spring training in. Logan made his Major League debut on April 4, 2006. During 2006, Logan made 21 relief appearances with 1 save despite splitting his time in the Minors but accumulated an 8.31 ERA in the Majors that year. In 2007, Logan made 68 relief appearances going 2-1 with a 4.97 ERA. In 2008, he made 55 appearances going 2-3 with a 5.95 ERA.
On December 22, 2009, Logan was once again traded along with Javier Vázquez, this time to the New York Yankees for Melky Cabrera, and prospects Michael Dunn and Arodys Vizcaíno. On April 16, 2010 Logan was called up by the Yankees to replace Chan Ho Park in the Yankee bullpen. In 2010, Logan made 51 relief appearances going 2-0 with a 2.93 ERA. In 2011, he made 64 relief appearances going 5-3 with a 3.46 ERA. Logan made an MLB-leading 80 relief appearances in 2012, going 7-2 with 1 save and a 3.74 ERA. In 2013, he made 61 appearances from the bullpen going 5-2 with a 3.23 ERA. On October 4, 2013, Logan underwent surgery in his left elbow to remove bone spurs. He became a free agent at the end of the season.
Colorado Rockies
Logan signed a three-year deal with the Colorado Rockies on December 16, 2013. On September 13, 2014, Logan again underwent surgery in his left elbow to remove a bone spur, abruptly ending his 2014 season. In 35 games, Logan went 2-3 with a 6.84 ERA. Logan was also on the Rockies for the 2015 and 2016 seasons.
On February 7, 2017, Logan signed with the Indians to a one-year contract with an option for the 2018 season. The Indians declined to exercise their club option on Logan's contract for the 2018 season on November 6, 2017, making Logan a free agent.
Milwaukee Brewers
On January 10, 2018, Logan signed a one-year deal with the Milwaukee Brewers worth $1.875 million. On June 19, Logan was designated for assignment and was released on June 24.
Pitching style
Logan throws with a sidearm delivery, making him appealing as a left-handed specialist. Left-handed hitters have batted only.247 against him in his career, while righties have hit.311. Logan is especially tough against lefties because his primary pitch is a slider in the low 80s that breaks sharply away from them. This is his favorite pitch to throw in two-strike counts. He also has a four-seam fastball and two-seam fastball that appear in the 92-95 mph range. Logan also throws a high-80s changeup from time to time against right-handers.
