Except as otherwise provided by Law or this Charter, the City Secretary shall give notice of the enactment of every ordinance imposing any penalty, fine, or forfeiture for any violation of any of its provisions, and of every other ordinance required by Law or this Charter to be published, by causing said ordinance, or its caption and penalty, to be published at least one time within ten days after final passage thereof in the official newspaper of the City. The affidavit of publication by the publisher of such newspaper taken before any officer authorized to administer oaths and filed with the City Secretary shall be conclusive proof of the legal publication and promulgation of such ordinance in all Courts.