Description:
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My PHP-FPM configuration works: I could run php-fpm with sudo php-fpm & command, and with ps aux | grep "php-fpm" I could see one master process running as root, and two daughter processes running as www-data user: (output stripped for convenience)

root      php-fpm: master process (/usr/local/etc/php-fpm.conf)
www-data  php-fpm: pool www
www-data  php-fpm: pool www

Webserver works perfectly as well.

BUG:

I heard somewhere that running PHP-FPM as a root could be potentially not good for security, so I decided to try to launch master process as www-data user:

su -c "php-fpm &" -s /bin/sh www-data

But, it returns an error:

ERROR: failed to open error_log (/usr/local/var/log/php-fpm.log):
  Permission denied (13)
ERROR: failed to post process the configuration
ERROR: FPM initialization failed

I have tried to change permissions of php-fpm.log file and /usr/local/var/log folder, even to 777, also tried various owners with chmod command ( my current user, www-data, root, etc ) But, that does not eliminate an error