Python logging: create log if not exists or open and continue logging if it does

I'm writing some code that uses the python logging system. The idea is that if the LOG doesn't already exist create the log but if it does then get the log and resume logging to that file. Here is my code:

import logging
import os

log_filename='Transactions.log')
if os.path.isfile(log_filename)!=True:
    LOG = logging.getLogger('log_filename')
    LOG.setLevel(logging.DEBUG)
    # create file handler which logs even debug messages
    fh = logging.FileHandler('log_filename')
    fh.setLevel(logging.DEBUG)
    # create console handler with a higher log level
    ch = logging.StreamHandler()
    ch.setLevel(logging.DEBUG)
    # create formatter and add it to the handlers
    formatter = logging.Formatter('-->%(asctime)s - %(name)s:%(levelname)s - %(message)s')
    fh.setFormatter(formatter)
    ch.setFormatter(formatter)
    # add the handlers to the logger
    LOG.addHandler(fh)
    LOG.addHandler(ch)
else:
    LOG=logging.getLogger()

I suspect the problem is with my else block but I don't know how to fix. Could anybody shed some light on this situation.

The logging module's FileHandler takes care of that for you. No need for complexity.

The handler takes an optional mode parameter, to specify whether it starts writing or appending data to it.

From the docs:

class logging.FileHandler(filename, mode='a', encoding=None, delay=False)

The specified file is opened and used as the stream for logging. If mode is not specified, 'a' is used.