Generally I've found logging direct to a file very limiting (unless the app is running as a daemon and has no terminal). If run from the shell I prefer to redirect using the shell:

./some_script > /some/log
[download]

For directing both STDOUT and STDERR you could use this (bash):

./some_script >& /some/log
[download]

or this (shells that don't support >&):

./some_script > /some/log 2>&1
[download]

making sure to have turned on $| in your script of course.

That way you can see output on the terminal if you wish; filter it; send stdout to /dev/null; or just send all output to the log directly - some of which are difficult to do if your script itself is writing direct to the log.