I have an application, which keeps track of some logs since its installation time.
Since the system log may be huge, my application's performance is too bad if the log is too large, but if we cleared the log just before installation, it will be much much better.
I know it is not my right to do so, but for now I am searching for its security issues.
So, will it considered - regardless the ethics - danger clearing the log named "system" only?
You can if you want. There is no danger in deleting any of the logs, as they are only there for your records to help you diagnose issues.
If you are confident that you or anyone else using the computer won't need the system logs then go ahead and delete them.
If I were installing it on my machine I wouldn't want it doing this without my explicit permission though, so maybe have a message to explain to the user that it might run slow if you choose not to delete them.