PHP execute command and log output without waiting

I use exec() to execute command, either linux or windows.

How do you execute a command, linux and windows, and log the output without waiting?

I know for linux, to not wait for the output: command* > /dev/null 2>/dev/null &

And to log output for linux: command* > /path/to/log.txt 2>/path/to/error.txt

How would you go about logging and setting it to background in one command? How would windows look like too?