mysql logging activity from specific user or ip
You could use the general log. In fact, you should try using the MySQL table version of the general log.

If you run this:

SHOW CREATE TABLE mysql.general_log\G


You should see something like this:

mysql&gt; show create table mysql.general_log\G
*************************** 1. row ***************************
       Table: general_log
Create Table: CREATE TABLE `general_log` (
  `event_time` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
  `user_host` mediumtext NOT NULL,
  `thread_id` int(11) NOT NULL,
  `server_id` int(10) unsigned NOT NULL,
  `command_type` varchar(64) NOT NULL,
  `argument` mediumtext NOT NULL
) ENGINE=CSV DEFAULT CHARSET=utf8 COMMENT='General log'
1 row in set (0.14 sec)

mysql&gt;


The user_host column will record the MySQL user and the IP Address/DNS Name the command came from.

You are probably saying right now, "That table is a CSV file. I would have to parse it." That's true, you would have to. However, did you know that you can convert it to a MyISAM table? I have actually tried this out for one of my employer's DB Hosting Clients, and I wrote a post explaining it (See the Feb 24, 2011 post down below).

Here are the basic steps:


Make the mysql.general_log table MyISAM

Run the following:

CREATE TABLE mysql.general_log_original LIKE mysql.general_log;
ALTER TABLE mysql.general_log ENGINE=MyISAM;
ALTER TABLE mysql.general_log ADD INDEX (event_time);

Enable the general log 

Add the following to /etc/my.cnf

[mysqld]
log-output=TABLE
general-log


If you also want the text version of the general log, add this:

[mysqld]
log-output=TABLE,FILE
general-log
general-log-file=/var/log/mysql_general.log

Restart mysql

Simply run service mysql restart


I have many posts about using the general log and the slow log as MyISAM tables:


Jan 22, 2013 : How often does the slow_log table get updated in MySQL?
Nov 10, 2012 :  Redirecting MySQL errors and slow logs into another database
Jan 08, 2012 : How to enable MySQL general log?
Dec 27, 2011 : How to do MySQL User Accounting
Nov 18, 2011 : Create a custom log table in MySQL
Jun 30, 2011 : How do I output MySQL logs to syslog?
Feb 24, 2011 : Audit logins on MySQL database


CAVEAT

MySQL 5.5.28 has recently introduced the audit log plugin and how to install it.

Here are the options


audit-log-buffer-size
audit-log
audit-log-file
audit-log-flush
audit-log-policy
audit-log-rotate-on-size
audit-log-strategy


These are new to me so I have nothing pros or cons at this time on the Audit Log Plugin.