Is it legal for a security guard to record personal information on a log?

Yes, it is generally legal for security guards to record personal information in a log, as long as they comply with applicable laws and regulations regarding privacy and data protection. The specific legalities can vary by jurisdiction, and security personnel must ensure that they are not violating any privacy rights or laws, such as the General Data Protection Regulation (GDPR) in Europe or similar regulations elsewhere. It's important for security companies to have policies in place to manage how this information is collected, stored, and used.