Logan was born in Beverly Hills, to a Jewish family. His parents are Lisa (Goldman), who works as his manager, and Larry Lerman, an orthotist and businessman. He has two siblings, Lindsey and Lucas, both older. His relatives operate the orthotics and prosthetics company Lerman & Son, which was founded by his great-grandfather, Jacob Lerman.
When he was two and a half years old, Logan told his mother that he wanted to be an actor. 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: Le chemin de la liberté (2000). Also in 2000, he appeared with the same actor (Gibson), this time as the younger version of his character Nick Marshall, in Ce que veulent les femmes (2000). After a small role in 2001's Écarts de conduite (2001), he starred in John Grisham's A Painted House (2003).
Logan played the younger version of Ashton Kutcher's character, Evan, in L'effet papillon (2004). After making his small screen debut in a guest-starring role in Shérifs à Los Angeles (2003), he stared as Bobby (Robert) McCallister in the WB Network's series Jack & Bobby (2004), where he portrayed a teenager who will be a future president of the United States. After the show's cancellation in 2005, Logan returned to film, starring in the family adventure Hoot (2006). The next year, he played the son of Walter Sparrow (Jim Carrey) in the dark thriller Le nombre 23 (2007), and co-starred with Russell Crowe and Christian Bale in the well-reviewed Western remake 3h10 pour Yuma (2007). His next two roles were playing a foul-mouthed private school student in the comedy Meet Bill (2007) and a younger version of actor George Hamilton in the period drama Ma mère, ses hommes et moi (2009). Both were independent films that received limited releases. Also in 2009, Logan appeared with Gerard Butler in the R-rated action thriller Ultimate Game (2009), as a teenager who controls Butler's character in a real-life video game.
In 2010, Logan played the title character in the fantasy adventure Percy Jackson: Le voleur de foudre (2010), giving him notice among a wider audience. Subsequently, he starred as D'Artagnan in a remake of Les Trois Mousquetaires (2011), headlined Le monde de Charlie (2012), a film adaptation of the 1999 book of the same name, had a supporting role in the independent film L'amour malgré tout (2012), and returned to star in Percy Jackson: La mer des monstres (2013). His first 2014 role was in the epic Biblical film Noé (2014), playing one of the title character's sons, Ham; the film grossed over $100 million at the North American box office. Logan next starred with Brad Pitt, Shia LaBeouf, Jon Bernthal, and Michael Peña in the World War II-set action drama Fury (2014); in the film, he played one of several American soldiers engaged in tank combat against the German forces, during the last weeks of the Nazi regime.
Logan will next star as the lead, Marcus Messner, in the 1950s-set drama Indignation (2016), writer-director James Schamus's adaptation of Philip Roth's novel.
When Logan is not working, he likes to play soccer and baseball. He is an LA Lakers fan.
