The phrasal verbs log on and log in are interchangeable and mean to “connect to a computer system” (e.g., “The password didn’t work when I tried to log on to my online banking”).
The nouns log-on and log-in are also interchangeable and mean the details (e.g., username and password) that you need to access a system.
Log on (verb) and log-on (noun) are the most common variants in American English.
Knowing whether in vs on vs at is correct often depends on the specific context.
Use QuillBot’s free Grammar Checker to help you use these prepositions correctly in your writing.