Cuneiform writing is mostly logographic – usually, the meaning of the symbols is more important than the way they are pronounced. Some symbols were used phonetically, to spell out the names of kings and other important people. The pronunciation of these symbols was deciphered by comparing late cuneiform writing to early phonetic/alphabetic scripts, especially Old Persian.
Cuneiform writing was in use until as late as the 1st century BCE, while alphabetic writing was widespread by the 8th century BCE, so there is quite a bit of overlap.
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