From which prophet's writings did Daniel learn Jerusalem's desolation would last 70 years?

Answer: Jeremiah

Daniel understood from the word of the LORD to Jeremiah that the desolation of Jerusalem would last seventy years, and he turned to prayer.

“in the first year of his reign, I, Daniel, understood from the sacred books, according to the word of the LORD to Jeremiah the prophet, that the desolation of Jerusalem would last seventy years.”— Daniel 9:2 (BSB)