Whichever side you are on, you can accept the other side’s logic pertaining to the overall age of the universe. You may not agree with the day-age view, but it is clear that we base our belief in an old universe on the scientific data. Similarly, I do not agree with the 24-hour day interpretation, but I understand that if you do accept it, then the universe is only as old as mankind (plus five days), and the biblical genealogies will lead you to affirm an age of (approximately) ten thousand years.
While mathematically a much smaller discrepancy, the apparent age of mankind is much more troublesome. Scientific data seem to point to modern humans appearing about 50,000 years ago. This is five times bigger than the 10,000 year estimate from genealogies.
Keep in mind, that the day-age view affirms that Adam and Eve were the first humans, created by God by divine fiat, without human parents, and not descending from other primates. What the scientific data show is that Adam and Eve lived about 50,000 years ago.
I do not know how to reconcile this. I do know that biblical genealogies are not chronologically accurate, so there is a great opportunity for error in the genealogical calculations. For example, we have
Shebuel the son of Gershom, the son of Moses, was officer over the treasures. (1 Chron. 26:24)
Shebuel is of the time of David, and yet Gershom is a true next-generation son of Moses (Ex. 2:22) . Thus there are 400+ years between Gershom and his "son" Shebuel.
So it may be that this type of error has biased the biblical calculations toward a small result.
What is some of the scientific evidence? Again from Hugh Ross and Gleason L. Archer in The Genesis Debate (David G. Hagopian, ed., Cruxpress, 2001--see the book for further references):
- Mitochondrial DNA is inherited only from the mother (this may not be absolutely true, but no matter). By projecting variations in Mitochondrial DNA backward one can estimate when the first woman (Eve) lived; current calculations point to about 50,000 years ago.
- Similarly, Y chromosomes can studied to find our most recent common male ancestor (which is Noah, not Adam). The results are in the 37,000-49,000 year range.
- The oldest artifacts of advanced artwork are dated at about 32,000 years old.
- The Vela supernova, which bathed earth in harmful radiation, erupted 20,000 to 30,000 years ago.
- Land bridges enabling human migration to Australia appeared about 12,000 to 30,000 years ago and to the Americas about 11,000 to 14,500 years ago.
- The most ancient religious artifacts have been dated to about 8,000-24,000 years ago.
Thus biological, anthropological, and archeological evidence all point to the 50,000 year time frame.