3400 years.
The first thing to do is determine how many half lives the sample has undergone. Assuming that the level of atmospheric carbon 14 has remained consistent over time, the sample has only 2/3rd of the level of activity, so only has 2/3rds of the carbon-14 level. So calculate the logarithm to base 2 of 2/3.
log(2/3)/log(2) = -0.17609/0.30103 = -0.58496
This indicates that 0.58496 half lives have expired which is a reasonable number since if 1 half-life had been spent, the level of activity would be half of modern activity. So just multiply the number of half-lives by the half-life. So
-0.58496 * 5730 = -3351.835129
Rounding to 2 significant figures gives an estimated age of 3400 years.
