30% space in log file in private folder- can I delete it?

Yes.

Six ways to clean up your Mac​

 

Yes, it is a log file and probably went a bit psychopathic to become that big.
Look at the link I provided, though you don't need Onyx to do it, Finder can help you deleting log files too.

 

What is this "Other" in the storage tab? What is eating up my space? by theSeb

 

For space issues, there are a few things you can try, some of which may or may not apply:

• Begin by restarting your computer as a first step. This sometimes resolves issues.
• For Time Machine users on notebooks running Lion, space may being consumed by Time Machine local snapshots, which can be disabled.
  OS X Lion: About Time Machine's "local snapshots" on portable Macs
• Search with Finder to see if the space is being consumed by a very large file or several large files. Adjust the 50GB in the illustration to whatever size you deem appropriate.
  
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• Use OmniDiskSweeper, JDisk Report, Disk Inventory X or GrandPerspective to see how space is being used on your drive. Some of these apps may show more detail than others, so try several.

 

I just had a similar meltdown. I had 270 GB or so free on my 1 TB internal, and something started writing 25.4 log files into the "private" folder last Saturday night around midnight, every 30 seconds for at least 6 hours; something caused the last 4GB of space to be left alone (RAM swap file maybe?); I got rid of the logs (started from external) but only reclaimed about 1/2 the missing space, and absolutely could not locate it (using DiskInventoryX for all of this.) Noticed the hard drive writing furiously and found it was writing the log files again (or still.)
Had to try to find and back up recent files, wipe the drive, and restore from backup.

Very frustrating and time consuming (and very hard to not worry about it striking again.)

If you do happen to locate the rest of the missing space, and find a solution that does not involve erase/restore, please share!