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accomplishes the same thing without unzipping the whole file, and while i have never seen a log.tar.gz file that was a binary, i will concede that it might happen, so add the -a in there:
zgrep -ia "string" log.tar.gz
it's still shorter/easier to type...
This will extract all the apt-get install commands issued on the box, even if they are in the gzipped history files.
I use zgrep because it also parses non gzip files.
With ls -tr, we parse logs in time order.
Greping the empty string just concatenates all logs, but you can also grep an IP, an URL...
This command checks for the number of times when someone has tried to login to your server and failed. If there are a lot, then that user is being targeted on your system and you might want to make sure that user either has remote logins disabled, or has a strong password, or both. If your output has an "invalid" line, it is a summary of all logins from users that don't exist on your system.