1. To sign into one's account or computer. I'm having trouble logging into my computer, so I haven't had a chance to check my email yet. Make sure you log into your account on the website before you attempt to make a purchase.

2. To give someone access to an account or computer system. In this usage, a noun or pronoun can be used between "log" and "into." Can you log me into your computer? I need to check my email really quick, and my phone's battery is dead.