That path is for a *nix flavour system, where '~' refers to the users home directory. It's not applicable to Windows systems.
Headless server means a server with no direct input devices- no keyboard/mouse, no monitor- that's only used as a network server. Running the content server on Windows is not a headless configuration, assuming it's your desktop box you're talking about.
That said, I can't currently tell you the location of the content server logfile on Windows, because I'm not currently at home.
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