How to store Tornado logs to a file?

I've been facing issues where my server is throwing a 500 if the API isn't accessed for 30 mins at a stretch. To check the problem, I need to keep track of every single API request made. I'm using Tornado in front of Flask. This is my code so far:

import tornado.httpserver
import tornado.ioloop
import tornado.web
from flasky import app
from tornado.wsgi import WSGIContainer
from tornado.ioloop import IOLoop
from tornado.web import FallbackHandler

from tornado.log import enable_pretty_logging
enable_pretty_logging()


tr = WSGIContainer(app)

application = tornado.web.Application([
    (r".*", FallbackHandler, dict(fallback=tr)),
])

if __name__ == '__main__':
    application.listen(5000)
    IOLoop.instance().start()

Whats the most efficient way to store the logs to some file?

I tried doing this but it only works when the process exits with 0:

import sys
import time
timestr = time.strftime("%Y%m%d-%H%M%S")
filename = "C:/Source/logs/" + timestr + ".log"

class Logger(object):
    def __init__(self):
        self.terminal = sys.stdout
        self.log = open(filename, "a")

    def write(self, message):
        self.terminal.write(message)
        self.log.write(message)

    def flush(self):
        pass

sys.stdout = Logger()