Radioactive dating of fossils and other geologic samples works, up to a point. But there is a time-bomb of illogic, buried in the floor of the method. You could tell how old the earth is from the rate of radioactive elements breaking down in rocks, only if you presuppose that all radioactive elements start at "100%", i.e., their little selves haven't started shedding yet. But the only way you can only know that is if (a) God doesn't exist (but then the deeper question of why anything anywhere exists at all, since nothing comes from nothing, becomes inexplicable), or (b) if you just dogmatically assert, with no evidence but just as a raw assertion, that God definitely started every radioactive thing at 100%.
But if God planted radioactive elements into the world at all stages of decay -- just like He created whole forests with rings and burrowing bugs already in them, entire oceans full of already-living animals, and human beings already physically old enough to make babies -- then that torpedos the underlying logic of radioactive dating