Roger the Mole
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.]