Best Answer on this worked for me (log file not having permission to write on a new install), but it's worth pointing out to the people who were struggling with this and choosing an unsafe 777 work around:
www-data is not always the user running your webserver (apache, etc)
In my server's case (bitnami on AWS --doing a clean install, not using their pre-installed laravel) 'daemon' was the user needed for the 'group' permission.
The key is that your webserver's user ('www-data' in the Best Answer example) is able to write to the necessary folders. Setting the group to your SSH/SFTP access user might let YOU write to the folders/files you need, but not allow the webserver to do so.