Correct spelling, explanation: the term login emerged in the mid-20th century as computers and digital systems became more prevalent. It refers to the process of providing credentials to gain access to a computer system, network, or online service. The word log in this context comes from the idea of recording or keeping a log of activities or events. The word in is used here to indicate entry or access. Remember that login is a noun and log in is a phrasal verb.

Definition of login:
noun, an act of logging in to a computer, database, or system
To access your email, please enter your username and password in the login fields.
She couldn’t remember her login, so she requested a password reset to regain access to her account.

Collocations with login:
Some most commonly used collocations include:
1. Username and password login: refers to the traditional method of gaining access to an account by entering both a username and a password.
The website requires a username and password login for security.
2. Secure login: indicates a login process that prioritizes security measures to protect user accounts.
To prevent unauthorized access, always use a secure login method.
3. Social media login: indicates the option to use social media account credentials (e.g., Facebook or Google) to log in to a website or app.
You can create an account or use social media login for a quicker sign-up process.

Correct spelling, explanation: log in as a phrasal verb is a relatively modern term in the context of computing and technology. Its etymology is tied to the development of computer systems and user authentication methods. In this sense, log comes from the concept of recording or keeping a log of user activities, and in refers to entering or gaining access to a system. The noun login has a slightly different history. It originated as a term in the 20th century to describe the process of gaining access to a computer system or network. It is formed by combining log, meaning to record or keep a record, and in, indicating entry or access.