I am little bit confused by these three logger libraries. It seems like that they can do the similar thing in java logging...
Check out their home pages:
SLF4J - The Simple Logging Facade for Java (SLF4J) serves as a simple facade or abstraction1 for various logging frameworks (e.g. java.util.logging, logback, log4j) allowing the end user to plug in the desired logging framework at deployment time.
1) It is not itself a logging library, but a generic interface to one of many logging libraries.
Log4j 1.2 - Welcome to Apache log4j, a logging library for Java.
Logback - Logback is intended as a successor to the popular log4j project, picking up where log4j leaves off.
Log4j 2 - Apache Log4j 2 is an upgrade to Log4j that provides significant improvements over its predecessor, Log4j 1.x, and provides many of the improvements available in Logback while fixing some inherent problems in Logback's architecture.
At least, that's what they all say of themselves.