He was the fifth son of the printer Johann Georg Unger (October 26, 1715 in Goes bei Pirna – August 15, 1788 in Berlin) and his wife Susanna Katharine (maiden name: Strucken).
He took on an apprenticeship at the print shop of the Oberhof printer Georg Jacob Decker.
In 1779 Unger requested a print shop for himself and in January 1780 he was granted one.
From 1784 onward he attempted repeatedly to gain approval to publish what would have been Berlin’s first daily newspaper.
In 1802 Unger nonetheless became co-owner of the Vossische Zeitung.