The key prophesies of Christ are missing in the Masoretic text or subtly different from those in Septuagint but it was the latter that was in use by Jews at the time.
The 10th century oldest Masoretic Text found in a Moscow synagogue agree perfectly with the pre-Christian Qumran copies of Isaiah.
Septuagint, on the other hand is a hypothetical entity because we only scanty parts of the pre-Christian Septuagint, but the other existing remnant are all Chritsian-era attempts to bring it to a closer agreement with the Mesoretic Text and are 2nd century AD work of Jewish scribes.
Apostolic writings quote solely from the Septuagint. Paul must have learned the Septuagint in his rabbinical training
They quote mostly form it (over 93% of the time) simply because Gospels were written in Greek. Jewish Encyclopedia very effectively debunks the myth that Paul had any formal rabbinical training.
The Septuagint was written well before the time of Christ and was considered to be of divine origin by non-Christian sources such as Josephus and Philo. The NT, with Septuagint quotes, was written the First Century.
AND THOU, BETHLEHEM Ephrata, art a little one among the thousands of Juda: out of thee shall he come forth unto me that is to be the ruler in Israel: and his going forth is from the beginning, from the days of eternity. (Micah 5:2)
10 And the Lord spoke again to Achaz, saying: 11 Ask thee a sign of the Lord thy God either unto the depth of hell, or unto the height above. 12 And Achaz said: I will not ask, and I will not tempt the Lord. 13 And he said: Hear ye therefore, O house of David: Is it a small thing for you to be grievous to men, that you are grievous to my God also? 14 Therefore the Lord himself shall give you a sign. Behold a virgin shall conceive, and bear a son, and his name shall be called Emmanuel [meaning "God is with us"]. (Isaiah 7)
Where the Septuagint uses the word "virgin," the Mesoretic text uses the Hebrew word for "maiden" which can mean young woman or, more traditionally, young virgin. The Septuagint indicates that translators understood the Hebrew word to be the equivalent of the "virgin" meaning for maiden. Note the context that clearly demonstrates the birth will be a special sign from God.