The half-life of carbon-14 is 5600 years. if a piece of charcoal made from the wood of a tree shows only 66% of the carbon-14 expected in living matter, when did the tree die?

3400 years The first thing to do is calculate how many half-lives that the sample has undergone. So basically, we have the following equation that we need to solve for X. 2^(-X) = 0.66 So what we're looking for is the logarithm to base 2 of 0.66, Since we can convert logarithms from in any base to a specified base by dividing by the logarithm of the desired base, we have log(0.66)/log(2) = -0.180456064 / 0.301029996 = -0.59946207 So -X = -0.59946207, and X = 0.59946207, which tells us that a bit over one half of a half life has expired which makes sense since there's more than one half of the original carbon-14 left. Now to get the years, multiply the half-life by the number of half-lives expired, getting 5600 * 0.59946207 = 3356.987594 years Rounding to 2 significant figures gives us 3400 years.