Logan wanted to become an actor at an early age, and he told his mother of his desire to be an actor when he was two and a half years old. At the age of four, Logan had an agent and was booked for two commercials. His first appearance on the big screen was as

William, the youngest son of Mel Gibson's character in
The Patriot (2000). Also in 2000, he appeared with the same actor (Gibson); this time as the younger version of his character Nick Marshall, in
What Women Want (2000). After taking on the role of Drew Barrymore's son in
Riding in Cars with Boys (2001), he starred in the film adaption of John Grisham's,
A Painted House (2003) (TV).
A breakout role for Logan was his portrayal of the younger version of Ashton Kutcher's character in The Butterfly Effect (2004). After making his small screen debut in a guest-starring role in 10-8: Officers On Duty (2003), he starred as Bobby (Robert) McCallister in Jack and Bobby (2004), where he portrayed a preteen who would be the future president of the United States. Continuing with his feature film work, Logan starred in Hoot (2006) alongside actors such as Luke Wilson, Brie Larson and Cody Linley. The film earned him a Young Artist Award for Best Performance in a Feature Film - Leading Young Actor.
Jim Carrey, had always been, and still remains to be, one of the most influential actors for Logan. At the age of fourteen, he appeared in the thriller, The Number 23 (2007), alongside the experienced Canadian actor. In the same year, he appeared in the western drama, 3:10 to Yuma (2007), which earned him another nomination for a Young Artist Award for Best Performance in a Feature Film - Leading Young Actor. More recent, and notable, starring roles for Logan are Gamer (2009), co-starring with Gerard Butler, and My One and Only (2009), with big names such as Renée Zellweger and Kevin Bacon. His most recent work on the silver screen, however, is in Percy Jackson and the Olympians: The Lightning Thief (2010), where he portrays the main character from the popular children's book series. As the books have been compared to the very successful Harry Potter series, Logan told Teen Vogue magazine, "Honestly, my character doesn't have much in common with Harry Potter besides the fact that he's an unlikely hero who's thrown into a huge situation."
When Logan is not working, he enjoys playing soccer and baseball. He is an LA Lakers fan and, even though he plays mostly dramatic roles, he enjoys playing pranks on his friends. Logan and his best friend Dean Collins often make comedic short films which can be seen on YouTube under the username, monkeynuts1069. The two have also formed their own band with Daniel Pashman titled Indigo. Logan plays the keyboard and the guitar.