The OPA0/tty00 and TTA0/tty01 ports each provide an Avanti serial-output logging option, disabled by default in a new configuration. Enable Log file on the port's configuration tab and choose its own file name. A fresh current log is created when the emulator starts, with predecessor retention controlled by versions. These files can grow large during a long run.
Avanti records serial output, not a separate copy of all terminal input; typed text appears when the guest echoes it. See Serial Port Logging for details. Client-side capture is a separate facility described under PuTTY Log Files.