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This is an interesting question. Scientists use carbon and other dating processes but overlook one detail. Because they are not believing God created the earth, they can't accept that God created everything in maturity. He didn't create Adam as a baby, he didn't grow a chicken from an egg. The point is, a scientist can judge a rock's age to be 3 million years old, but God could have put a 3 million year old rock there 7000 years ago.
All that being said, is knowing how old the earth is, necessary for our faith? Did Jesus ever say, "believe in me but if you don't know how old the earth is, you are doomed? No, some people just want to know if God's word is true by determining if the story of creation is scientifically possible.
Anything is possible with God. Must we scientifically prove the Red Sea parted, the Lazarus was resurrected, that Jesus walked on water, turned water to wine, and walked out of his own tomb, to believe?