Radioactive decay products in different rocks. The same 'theory' that runs nuke plants and makes bombs go boom also enables one to detrmine the decay products and determine how long they were there. Based upon these observations, the age of rocks are established. Also see all the articles on the natural reactor found in Africa. This planet is very, very old and no amount of biblical literalism can erase that fact. I also speak as a christian conservative. Until you can disprove nuclear theory, you will have absolutely no basis for stating that the Earth is less than 10,000 years old.
and BTW....measurement error and assumptions gives an uncertainty of 10% or so. Heck even at 50% uncertainty it would still be at least 2,000,000 yrs old at minimum.
And of course science is infallible. Wouldn't want to make so-called scientists appear to be wrong. How could they make money on their teachings and books and government grants?