A fabric remnant from a burial site has a 14c/12c ratio of 0.662 of the original value. how old is the fabric?

The half-life of carbon-14 is 5730 years, so you have
.. 0.662 = 2^(-t/5730) . . . . . . . . . . . . . . . . . t is age in years (before present)
.. log(0.662) = -t/5730*log(2)
.. t = -5730*log(0.662)/log(2) ≈ 3410 . . . . years