With Misa Amane's introduction to Light, he agrees to use her and to pretend to be her boyfriend if she can get L's true name and help him kill him.  He also learns from Misa how a Shinigami can be killed.  L confides in Light that he just might be the first true friend that he's ever had.  This doesn't stop Light from trying to kill him still.  Light realizes that Rem, Misa's Shinigami, is in love with her after she says she will kill Light if anything would happen to Misa.  He uses this to get Rem to kill L with her notebook but has her promise not to do anything until Light gives the word.