You would have to first determine the current state of the database by using the eseutil /mh. If the database is in a clean shutdown state, you could mount the database without the logs and it would start new log generation (it would give you an alert to this). The only data you would lose of course is anything within the log files that were not committed and lost.
if the database is in a dirty shutdown state, you would need to restore the database from backup. your data loss would be everything after the backup.