The fact that you take them from the medicine cabinet at work means that the company can keep this log: in taking the medication from supplies your employer maintains (and has to refill; and is potentially liable for misuse of), you give up your expectation of privacy vis-a-vis them. If you want to keep this information private, don't use the workplace medicine cabinet--bring the supplies, medications, etc. from home. As alluded to above, the company has at least two legitimate reasons to keep this log: first, to know when to refill the supplies; and second, the information should be kept in case someone abuses, misuses, has a bad reaction to, etc. the medication, any of which could potentially make the company liable.