Me and my friend were trying to decide just how good of a detective L from Death Note is, could he find out that Bruce Wayne is indeed Batman?? 
 
SCENARIO-  
 
Batman is on the run from the law, they still consider him a dangerous vigilante, the GCPD hires L, who is known as the world's greatest detective to figure out who Batman is, and help bring him in, can L do it? or is Batman to smart to get caught?? 
 
 

It's plausible that L could indeed find out Batman's true identity, but bringing him in is highly unlikely.

To state the obvious, yes. He can uncover pretty much any person under a mask whether it be Batman, Cyclops, Night Thrasher, Moon Knight, Juggernaut, Spiderman, Grifter. Even people who don't have mask like able to tell if Clark Kent is Superman.

Would he be able to know who Batman is? Yes. The question is, in the scenario provided, would Batman allow himself to be known? What I mean is, would Batman be allowed to strike him down before he gets to investigate who Bats is...

Would he be able to know who Batman is? Yes. The question is, in the scenario provided, would Batman allow himself to be known? What I mean is, would Batman be allowed to strike him down before he gets to investigate who Bats is...

L has never left a case unsolved....He manged to find out light was kira he just didn't have evidence on him...L would find bruce wayne in a week

He would profile suspects and will choose Bruce Wayne as a likely candidate.It's happened before in year one.