No, Artaxerxes was not the king of Babylon; he was actually the king of Persia. Specifically, there were two notable Persian kings named Artaxerxes: Artaxerxes I (reigned from 465 to 424 BC) and Artaxerxes II (reigned from 404 to 358 BC). These rulers were part of the Achaemenid dynasty, which was known for its vast empire that spanned various regions, including parts of the modern-day Middle East.
While Babylon was an important city within the Persian Empire, it was not ruled by its own kings during this period. Instead, it fell under the control of the Persian kings, including Artaxerxes. Babylon had its own local rulers, known as governors or satraps, who were appointed by the Persian monarchy.
In summary, Artaxerxes was a significant figure in Persian history, but he was not a king of Babylon itself.