A different approach to your basic need is something I used for managing more than 100 UNIX systems (many kinds of OS) in a large computing facility: send the log per email.
Create a cron job (Linux: /etc/cron.daily/sendlog) which extract the interesting information from all log files, and then e-mail that to you. The extraction filters need some adaption to your specific needs, to reduce the number of lines. The only thing you have to do is browse through the mails, first thing every morning.
In larger UNIX/Linux environments, you can also decide to configure syslog to send reports directly to syslog daemons on other systems (nick one of your systems as 'loghost'). This way, you can collect data from multiple systems in one file, which is easier to maintain.