Log of all calls made by modem

Does my computer have a log of all calls made by my modem? Where can I find this log?

You don’t mention your OS so these steps may vary.
In Win98SE click the Start button, highlight Settings, click Control Panel and double-click Modems. On the General tab of Modem Properties highlight a modem and click the Properties button. On the Connection tab click Advanced… In the Advanced Connection Settings click View Log.

You have to enable logging on many WinOSes or the log will be empty. There are many freeware programs that log dial-outs, though I don’t know how thorough they each of them is. Any software firewall on your modem connection [advised!] may have a more convenient dialing log which should be well integrated with the OS to prevent unlogged “low level” dialing from escaping notice, though there was a time when “low level dialing” (sending standard Hayes AT codes to serial ports, instead of using the modem routines) sometimes snuck under logging.