When we talk about "logging time", we usually mean keeping track of the hours we spend on a particular task or project. However, there are plenty of synonyms that capture this concept in various ways. For example, you might "clock in" or "punch a time card" to indicate that you've started work. Alternatively, you could "monitor your hours" or "track your progress" to keep tabs on how much time you're spending. If you're billing by the hour, you might "tally your time" or "account for your hours". Whatever phrase you choose, the idea is the same: you're making sure that your time is being used effectively and efficiently.