I currently have a log file which has no limit and I was hoping to be able to set up a cron job that would start writing to a new file so it doesn't get too big. Would that be possible? So it would keep the old one with a date and start a new one, with a 10MB size limit.
This problem is common enough that there's a whole program to do that, logrotate, which can also zip the old files, only keep the last X, and pretty much most things you could reasonably want to do with old logfiles.
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logrotate. Hard not to find that with a short look at your favorite search engine.