Absolutely. I'd speculate that you have a program in your Startup folder that runs every time you turn on your computer. This program probably created that log file and placed it there because that's the folder the program is in. So every time you turn on your computer, that log file is opening.
It's 100% safe to delete.
To keep the problem from happening again, I'd ask: do you indeed have a program in your Startup folder that is running every time you turn on your computer? if so, move that program somewhere else, then put a shortcut to it in the Startup folder instead. Then any log file will be created somewhere else, away from the Startup folder.