Backup SQL Server 2016 Instance Logins
In General

I would consider reading up on what information the master database contains and why you need to backup the system databases (master, msdb, ...).

Reference: Back Up and Restore of System Databases (SQL Server) (Microsoft Docs)

master Database

The master database contains the following information for each SQL Server instance:


  The master database records all the system-level information for a SQL Server system. This includes instance-wide metadata such as logon accounts, endpoints, linked servers, and system configuration settings. In SQL Server, system objects are no longer stored in the master database; instead, they are stored in the Resource database. Also, master is the database that records the existence of all other databases and the location of those database files and records the initialization information for SQL Server. Therefore, SQL Server cannot start if the master database is unavailable.  


(emphasis mine)

Reference: master Database (Microsoft Docs)

msdb Database

The msdb database contains the following information of a SQL Server instance:


  The msdb database is used by SQL Server Agent for scheduling alerts and jobs and by other features such as SQL Server Management Studio, Service Broker and Database Mail.
  
  For example, SQL Server automatically maintains a complete online backup-and-restore history within tables in msdb. This information includes the name of the party that performed the backup, the time of the backup, and the devices or files where the backup is stored. SQL Server Management Studio uses this information to propose a plan for restoring a database and applying any transaction log backups. Backup events for all databases are recorded even if they were created with custom applications or third-party tools. For example, if you use a Microsoft Visual Basic application that calls SQL Server Management Objects (SMO) objects to perform backup operations, the event is logged in the msdb system tables, the Microsoft Windows application log, and the SQL Server error log. To help your protect the information that is stored in msdb, we recommend that you consider placing the msdb transaction log on fault tolerant storage.  


(emphasis mine)

Reference: msdb Database (Microsoft Docs)

Conclusion

If you backup the master database, then all the login information for the instance is safe. However, if you want to separately back up (as in: used to transfer logins to different instances, used to reset passwords) the SQL Logins of the instance, then you would have to apply a different solution.

Individual SQL Server Login Backup Solutions

Tool Reference List


dbatools.io (dbatools.io)


Copy-DbaLogin
Export-DbaLogin
Copy-DbaCredential
Copy-DbaAudit

Transfer Login Task (Microsoft Docs)


Added bonus


How to transfer logins and passwords between instances of SQL Server (Microsoft KB article)


The last reference is an interesting article on how to manually export the SQL Server logins and the hashed passwords in order to manually transfer them to a a new SQL Server instance. The article involves creating two stored procedures and then running one to create the information.

Here is the code from the refercned article to create the two procedures:

USE master
GO
IF OBJECT_ID ('sp_hexadecimal') IS NOT NULL
  DROP PROCEDURE sp_hexadecimal
GO
CREATE PROCEDURE sp_hexadecimal
    @binvalue varbinary(256),
    @hexvalue varchar (514) OUTPUT
AS
DECLARE @charvalue varchar (514)
DECLARE @i int
DECLARE @length int
DECLARE @hexstring char(16)
SELECT @charvalue = '0x'
SELECT @i = 1
SELECT @length = DATALENGTH (@binvalue)
SELECT @hexstring = '0123456789ABCDEF'
WHILE (@i &lt;= @length)
BEGIN
  DECLARE @tempint int
  DECLARE @firstint int
  DECLARE @secondint int
  SELECT @tempint = CONVERT(int, SUBSTRING(@binvalue,@i,1))
  SELECT @firstint = FLOOR(@tempint/16)
  SELECT @secondint = @tempint - (@firstint*16)
  SELECT @charvalue = @charvalue +
    SUBSTRING(@hexstring, @firstint+1, 1) +
    SUBSTRING(@hexstring, @secondint+1, 1)
  SELECT @i = @i + 1
END

SELECT @hexvalue = @charvalue
GO

IF OBJECT_ID ('sp_help_revlogin') IS NOT NULL
  DROP PROCEDURE sp_help_revlogin
GO
CREATE PROCEDURE sp_help_revlogin @login_name sysname = NULL AS
DECLARE @name sysname
DECLARE @type varchar (1)
DECLARE @hasaccess int
DECLARE @denylogin int
DECLARE @is_disabled int
DECLARE @PWD_varbinary  varbinary (256)
DECLARE @PWD_string  varchar (514)
DECLARE @SID_varbinary varbinary (85)
DECLARE @SID_string varchar (514)
DECLARE @tmpstr  varchar (1024)
DECLARE @is_policy_checked varchar (3)
DECLARE @is_expiration_checked varchar (3)

DECLARE @defaultdb sysname

IF (@login_name IS NULL)
  DECLARE login_curs CURSOR FOR

      SELECT p.sid, p.name, p.type, p.is_disabled, p.default_database_name, l.hasaccess, l.denylogin FROM 
sys.server_principals p LEFT JOIN sys.syslogins l
      ON ( l.name = p.name ) WHERE p.type IN ( 'S', 'G', 'U' ) AND p.name &lt;&gt; 'sa'
ELSE
  DECLARE login_curs CURSOR FOR


      SELECT p.sid, p.name, p.type, p.is_disabled, p.default_database_name, l.hasaccess, l.denylogin FROM 
sys.server_principals p LEFT JOIN sys.syslogins l
      ON ( l.name = p.name ) WHERE p.type IN ( 'S', 'G', 'U' ) AND p.name = @login_name
OPEN login_curs

FETCH NEXT FROM login_curs INTO @SID_varbinary, @name, @type, @is_disabled, @defaultdb, @hasaccess, @denylogin
IF (@@fetch_status = -1)
BEGIN
  PRINT 'No login(s) found.'
  CLOSE login_curs
  DEALLOCATE login_curs
  RETURN -1
END
SET @tmpstr = '/* sp_help_revlogin script '
PRINT @tmpstr
SET @tmpstr = '** Generated ' + CONVERT (varchar, GETDATE()) + ' on ' + @@SERVERNAME + ' */'
PRINT @tmpstr
PRINT ''
WHILE (@@fetch_status &lt;&gt; -1)
BEGIN
  IF (@@fetch_status &lt;&gt; -2)
  BEGIN
    PRINT ''
    SET @tmpstr = '-- Login: ' + @name
    PRINT @tmpstr
    IF (@type IN ( 'G', 'U'))
    BEGIN -- NT authenticated account/group

      SET @tmpstr = 'CREATE LOGIN ' + QUOTENAME( @name ) + ' FROM WINDOWS WITH DEFAULT_DATABASE = [' + @defaultdb + ']'
    END
    ELSE BEGIN -- SQL Server authentication
        -- obtain password and sid
            SET @PWD_varbinary = CAST( LOGINPROPERTY( @name, 'PasswordHash' ) AS varbinary (256) )
        EXEC sp_hexadecimal @PWD_varbinary, @PWD_string OUT
        EXEC sp_hexadecimal @SID_varbinary,@SID_string OUT

        -- obtain password policy state
        SELECT @is_policy_checked = CASE is_policy_checked WHEN 1 THEN 'ON' WHEN 0 THEN 'OFF' ELSE NULL END FROM sys.sql_logins WHERE name = @name
        SELECT @is_expiration_checked = CASE is_expiration_checked WHEN 1 THEN 'ON' WHEN 0 THEN 'OFF' ELSE NULL END FROM sys.sql_logins WHERE name = @name

            SET @tmpstr = 'CREATE LOGIN ' + QUOTENAME( @name ) + ' WITH PASSWORD = ' + @PWD_string + ' HASHED, SID = ' + @SID_string + ', DEFAULT_DATABASE = [' + @defaultdb + ']'

        IF ( @is_policy_checked IS NOT NULL )
        BEGIN
          SET @tmpstr = @tmpstr + ', CHECK_POLICY = ' + @is_policy_checked
        END
        IF ( @is_expiration_checked IS NOT NULL )
        BEGIN
          SET @tmpstr = @tmpstr + ', CHECK_EXPIRATION = ' + @is_expiration_checked
        END
    END
    IF (@denylogin = 1)
    BEGIN -- login is denied access
      SET @tmpstr = @tmpstr + '; DENY CONNECT SQL TO ' + QUOTENAME( @name )
    END
    ELSE IF (@hasaccess = 0)
    BEGIN -- login exists but does not have access
      SET @tmpstr = @tmpstr + '; REVOKE CONNECT SQL TO ' + QUOTENAME( @name )
    END
    IF (@is_disabled = 1)
    BEGIN -- login is disabled
      SET @tmpstr = @tmpstr + '; ALTER LOGIN ' + QUOTENAME( @name ) + ' DISABLE'
    END
    PRINT @tmpstr
  END

  FETCH NEXT FROM login_curs INTO @SID_varbinary, @name, @type, @is_disabled, @defaultdb, @hasaccess, @denylogin
   END
CLOSE login_curs
DEALLOCATE login_curs
RETURN 0
GO


Once you have create the stored procedures run sp_help_rev_login to retrieve the information.

EXEC sp_help_revlogin



  The output script that the sp_help_revlogin stored procedure generates is the login script. This login script creates the logins that have the original Security Identifier (SID) and the original password.


Reference: How to transfer logins and passwords between instances of SQL Server (Microsoft KB article)

Enjoy