If a mineral has a daughter to parent ration of 3:1 (three daughter atoms for every one parent atom), how many half-lives have passed since the mineral formed?

The answer to this question would be: 2 half-lives

In this question, the mineral has a daughter to parent ratio of 3:1. That means, the amount of parent mass should be are 1 / (3+1) = 1/4 of the total mass. For every half live, the parent mass would become 1/2. Then for 1/4, the number of half-lives should be:

1/2^x = 1/4

1/2^x = 1/2^2

x=2