I have been trying for a whole day to figure out how to redirect 404 errors to a separate log file. I managed to do this in the server directive:

error_page 404 = @404;
location @404 {
error_log /var/log/nginx/404.log;
}

This does write all 404 errors to 404.log, but the problem is that it also writes these errors in the default error.log, and I don't want that. I want 404 errors to be writtent to only into the 404.log.

Do you have an idea how to do this?