How to manage error_log and access_log of apache?

You can use a utility such as cronolog to manage the web server log files. Using cronolog, log files can be automatically rotated without having to shut down and restart the web server.

excerpt

cronolog is a simple filter program that reads log file entries from standard input and writes each entry to the output file specified by a filename template and the current date and time. When the expanded filename changes, the current file is closed and a new one opened. cronolog is intended to be used in conjunction with a Web server, such as Apache, to split the access log into daily or monthly logs.

You can use logrotate, which allows you to rotate the logs (based on the date, the size...) and to choose how many files you want to keep. For instance, here's my config file for apache:

/var/log/apache2/*.log {
        weekly
        missingok
        rotate 52
        compress
        delaycompress
        notifempty
        create 640 root adm
        sharedscripts
        postrotate
                if /etc/init.d/apache2 status > /dev/null ; then \
                    /etc/init.d/apache2 reload > /dev/null; \
                fi;
        endscript
}