One more try ...
SELECT *, COALESCE((a.magnitude / g.generated), 0) AS result
FROM
(
SELECT COUNT(*) AS generated
FROM logs
INNER JOIN generated_logs
ON generated_logs.log_fk = logs.log_pk
WHERE logs.department_fk = ?
AND DATE(generated_logs.generated_time) = ?
) AS g,
(
SELECT COUNT(generated_logs.log_fk) AS magnitude, logs.name
FROM logs
INNER JOIN generated_logs
ON generated_logs.log_fk = logs.log_pk
WHERE logs.department_fk = ?
AND generated_logs.acknowledged = 1
AND DATE(generated_logs.generated_time) = ?
GROUP BY generated_logs.log_fk
ORDER BY magnitude DESC
LIMIT 1
) AS a