There are two cases, using ksh as your shell, then you need to do IO redirection accordingly, and using some other shell and executing a .ksh script, then IO redirection could be done based on that shell. Following method should work for most of the shells.
$ cat somescript.ksh
#!/bin/ksh -x
printf "Copy file \n";
printf "Do something else \n";
Run it:
$ ./somescript.ksh 1>some.log 2>&1
some.log will contain,
+ printf 'Copy file \n'
Copy file
+ printf 'Do something else \n'
Do something else
In your case, no need to specify logfile and/or tee. Script would look something like this,
#!/bin/ksh -x
printf "copying file\n"
scp -i key user@server /path/to/file
exit 0
Run it:
$ ./myscript 1>/path/to/logfile 2>&1
2>&1 captures both stderr and stdout into stdout and 1>logfile prints it out into logfile.
Logfile= path.log.dateis a bug. You cannot have spaces in an assignment in shell. It should beLogfile=path.log.date. This isn't your actual script is it? (You have some case sensitivity issues too)