In SDL Tridion 2011 the existing logging framework (which required a logging section in each configuration file), has been replaced by the Logback logging framework.
You have to make sure to remove all of the following JAR files before upgrading:
The fact that something is still looking for
com.tridion.logging.LogFactory indicates you still have old (version 2009) JARs somewhere in the classpath (or in memory).
More details about the upgrade process for Content Delivery can be found in the documentation (requires login).
Also make sure that any custom implementations and add-on products are upgraded accordingly, if your Content Delivery implementation (or any of the add-ons you are using in there) is depending on the old logging framework, it should be upgraded (for a custom implementation this might mean you need to rewrite its code) to use the new logging framework.