<span>9370 years
First, you need to determine how many half-lives the sample has undergone. Since 67.7% has been lost, that means that 100% - 67.7% = 32.3% has been retained. So calculate the logarithm to base 2 of 0.323:
log(0.323)/log(2) = -0.490797478/0.301029996 = -1.63039393
The number -1.63039393 tells you that 1.63039393 half-lives have occurred since the mastodon died. A quick sanity check will assure you that this is true. Because after 1 half live, there would be 50% of the carbon-14 remaining. And after another half life, there would be 25% of the original carbon-14 remaining. And since 32.3% is between 25% and 50%, the value of 1.63 half lives is quite reasonable. Now just multiply the number of half lives expended by the half life of carbon-14.
1.63039393 * 5750 = 9374.765097
Rounding to 3 significant figures gives us 9370 years.</span>
This is because Avogadro constant refer to the number of molecules or atoms of particles per mile substance and thus is equal to 6.022×10^23 per mile or unit of that substance.