we plan to use FIM for password sync.

Is it possible to detect password change request from PCNS angent by FIM server and write some log file  ? 

Not exactly - you can create dummy MA and configure it as password synchronization target, then use this agent password extension to write some log file. For such MA you can use SQL MA to not create something specific with custom password synch extension

BTW: PCNS and Synch engine which receives PCNS calls has event logging mechanism built-in. Why not gather events from event log? 

Thank you.

If we prepare target AD_MA and specify prefered DC,

the event is recoreded to prefered DC event when password sync happened ?

+1 for Tomek's answer; you could use my PowerShell MA as it supports PCNS (http://blog.goverco.com/p/powershell-management-agent.html

Thank you.

How about the below ?

I guess creating new MA needs more time to evaluate. 

>If we prepare target AD_MA and specify prefered DC,

>the event is recoreded to prefered DC event when password sync happened ?