With DEBUG=False, how can I log django exceptions to a log file

Django uses a logging filter to decide wither the console handler is used or not by default. See also django.utils.log on Github.

To keep the same behavior without filtering messages to console, just disable filtering in your settings.py like this:

from django.utils.log import DEFAULT_LOGGING

DEFAULT_LOGGING['handlers']['console']['filters'] = []

Here's another way of doing it with complexity half-way between the other answers, logs both to console and file

# settings.py
LOGGING = {
    'version': 1,
    'disable_existing_loggers': False,
    'handlers': {
        'console': {
            'class': 'logging.StreamHandler',
        },
       'file': {
           'level': 'DEBUG',
           'class': 'logging.FileHandler',
           'filename': 'log.django',
       },
    },
    'loggers': {
        'django': {
            'handlers': ['console','file'],
            'level': os.getenv('DJANGO_LOG_LEVEL', 'DEBUG'),
        },
    },
}

Here is a full working logging configuration. Critical errors are logged to sentry, warnings are sent to admins by emails, normal notice errors are logged to syslog, and debug messages are prompted on the standard output.

LOGGING = {
    'version': 1,
    'disable_existing_loggers': False,
    'filters': {
        'require_debug_false': {
            '()': 'django.utils.log.RequireDebugFalse'
        }
    },
    'formatters': {
        'verbose': {
            'format': '[contactor] %(levelname)s %(asctime)s %(message)s'
        },
    },
    'handlers': {
        # Send all messages to console
        'console': {
            'level': 'DEBUG',
            'class': 'logging.StreamHandler',
        },
        # Send info messages to syslog
        'syslog':{
            'level':'INFO',
            'class': 'logging.handlers.SysLogHandler',
            'facility': SysLogHandler.LOG_LOCAL2,
            'address': '/dev/log',
            'formatter': 'verbose',
        },
        # Warning messages are sent to admin emails
        'mail_admins': {
            'level': 'WARNING',
            'filters': ['require_debug_false'],
            'class': 'django.utils.log.AdminEmailHandler',
        },
        # critical errors are logged to sentry
        'sentry': {
            'level': 'ERROR',
            'filters': ['require_debug_false'],
            'class': 'raven.contrib.django.handlers.SentryHandler',
        },
    },
    'loggers': {
        # This is the "catch all" logger
        '': {
            'handlers': ['console', 'syslog', 'mail_admins', 'sentry'],
            'level': 'DEBUG',
            'propagate': False,
        },
    }
}