I'm not certain, but I doubt I'd want to have an entire log file in my db under the Extension Attributes section. We have some EAs that are multiple lines of information, but that's not the same as the contents of a log file, some of which can be 1000s of lines long.
You may be better off using the API in a script to upload the target log file as an attachment.
Take a look at this thread, about the 8th post down, I explain how you can upload a file as an attachment to a computer's record using the Casper Suite API.
You should then be able to download that attachment from the Attachments section later. Now, granted, using that method won't allow you to do any searches against it, but, searching against an entire log file contained in the database would probably be pretty painful anyway, and may just time out on you.