I, and other Christians who have no trouble believing the earth is billions of years old, probably have very little scientific knowledge, or even scientific interest. Thats certainly the case with me.
This rests on two points -
1). The very heavy weight of professionals who study this sort of thing for a living. Can someone find an article anywhere where any professional scientist/geologist states the Earth is probably 6,000 or so years old? Just one? Talking to a Baylor geology major at the Baylor game, he told me not a single professor or grad student in the department, to his knowledge, believed in a 6,000 year old Earth. He was a "fundamentalist" who thought it was absurd (although he was an undergrad).
2). The notion that the Earth is billions of years old and the notion that Genesis is true and correct (Adam and Eve were actual people, the flood was not a myth, and so on) are hardly incompatible. Why couldn't there have been other creations, for example? Because ours survived, even though it was very nearly destroyed?