Asample of bismuth-210 decayed to 33% of its original mass after 8 days
a) find the half-life of this element

The answer is 5 days

 (1/2)ⁿ = decimal amount remaining, where n i number of half-lives.

33% = 33/100 = 0.33 
(1/2)ⁿ = 0.33
log((1/2)ⁿ) = log(0.33)
n *log(1/2) = log(0.33)
n = log(0.33)/log(1/2) = log(0.33)/log(0.5) = -0.4815/-0.3010 = 1.6

Number of half-lives (x) is quotient of total time elapsed (t) and length of half-life:
x = 1.6
t = 8 days
x = t/half-life
half-life = t/x = 8 days / 1.6 = 5