The error_log files are generated within the 'path' of where the actual error is produced.
The error_log would be created in the domains public_html.
/home/USERNAME/public_html/error_log
If your website is on WordPress and the error was something that took place in the wp-admin (which is a directory of its own), then the error_log file would be in the wp-admin directory.
/home/USERNAME/public_html/error_log