You're not really giving enough information here but I'll have a go.
I'll assume that the 'default' log is standard out/err. If you actually have a 'default log' coded in your scripts, then you can modify the code below.
Code:
exec 3>&1
while getopts ":l:" opt; do
case ${opt} in
l) exec >${OPTARG} 2>&1;;
*) echo "Invalid argument supplied" >&3; exit 1;;
esac
done
shift $((OPTIND-1))
echo Stdout message >&1
echo Implicit stdout message
echo Stderr message >&2
echo Safe message to terminal >&3
e.g. yourScript -l aLogFile