How to see log files in MySQL?

I've read that Mysql server creates a log file where it keeps a record of all activities - like when and what queries execute. Can anybody tell me where it exists in my system? How can I read it? Basically, I need to back up the database with different input [backup between two dates] so I think I need to use log file here, that's why I want to do it... I think this log must be secured somehow because sensitive information such as usernames and password may be logged [if any query require this]; so may it be secured, not easily able to be seen? I have root access to the system, how can I see the log? When I try to open /var/log/mysql.log it is empty. This is my config file: [client] port = 3306 socket = /var/run/mysqld/mysqld.sock [mysqld_safe] socket = /var/run/mysqld/mysqld.sock nice = 0 [mysqld] log = /var/log/mysql/mysql.log binlog-do-db=zero user = mysql socket = /var/run/mysqld/mysqld.sock port = 3306 basedir = /usr datadir = /var/lib/mysql tmpdir = /tmp skip-external-locking bind-address = 127.0.0.1 # # * Fine Tuning # key_buffer = 16M max_allowed_packet = 16M thread_stack = 192K thread_cache_size = 8 general_log_file = /var/log/mysql/mysql.log general_log = 1