After 252 days a 40.0 gram sample of Scandium-42 contains only 2.5 grams of the isotope. What is the half-life of scandium?

Let "z" be the half-life (in days) to be found. 

Given:

2.5 g = 40.0 g x (1/2)^(252 days / z)

Solve for z algebraically:

2.5 / 40.0 = (1/2)^(252 days / z)

log (0.0625) = (log (1/2)) x (252 days / z)

log (0.0625) / log (1/2) = (252 days / z)

z = (252 days) / (log (0.0625) / log (1/2)) = 63 days

or

40.0 / 2 = 20.0

20.0 / 2 = 10.0

10.0 / 2 = 5.0

5.0 / 2 = 2.5

So exactly 4 half-lives have passed.

252 days / 4 = 63 days

[Although this number is nowhere near the accepted value for the half-life of Sc-42, which is measured in fractions of a second.  The closest you can get with Sc isotopes is 84 days with Sc-46.  The source below shows that there isn't really any known isotope with a half-life of 63 days.]