how to find out the start time of last sleep

You can use the pmset command to obtain this information. The following command obtains a log of the sleep/wake entries then restricts this to the last entry in the list which should be the most recent sleep:

pmset -g log | grep sleep | tail -n 1

You can obviously play around with anything after pmset -g log to give you what you need.

Actually, something like

pmset -g log|grep -e " Sleep  " -e " Wake  "

is what really gives me a clean timeline of sleep/wake events on 10.8.2. powerd does not log anything about it, at least on my system (10.8.2, MacBook Pro Retina 15).

02/03/13 19:48:37 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              26 secs   
02/03/13 19:49:03 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              27 secs   
02/03/13 19:49:30 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              26 secs   
02/03/13 19:49:56 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              26 secs   
02/03/13 19:50:22 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              26 secs   
02/03/13 19:50:48 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:99%)                              26 secs   
02/03/13 19:51:14 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:100%)                             1802 secs 
02/03/13 20:39:17 GMT-03 Sleep      Maintenance Sleep Sleep: Using BATT (Charge:100%)                           244 secs  
02/03/13 20:43:21 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:100%)                             51 secs   
02/03/13 21:07:17 GMT-03 Sleep      Maintenance Sleep Sleep: Using BATT (Charge:100%)                           242 secs  
02/03/13 21:11:19 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:100%)                             1103 secs 
02/03/13 21:29:42 GMT-03 Wake       Wake due to EC.LidOpen/Lid Open: Using AC (Charge:100%)                     
03/03/13 00:00:26 GMT-03 Sleep      Idle Sleep Sleep: Using BATT (Charge:85%)                                   96 secs   
03/03/13 00:02:02 GMT-03 Sleep      Maintenance Sleep Sleep: Using AC (Charge:85%)                              38 secs   
03/03/13 00:02:40 GMT-03 Wake       Wake due to EHC1/HID Activity: Using AC (Charge:85%)                        4338 secs 
03/03/13 01:14:58 GMT-03 Sleep      Clamshell Sleep to DarkWake: Using AC (Charge:100%)                         48382 secs
03/03/13 14:41:20 GMT-03 Wake       DarkWake to FullWake due to HID Activity: Using AC (Charge:100%)            728 secs  
03/03/13 14:53:28 GMT-03 Sleep      Clamshell Sleep to DarkWake: Using AC (Charge:100%)                         415 secs  
03/03/13 15:00:23 GMT-03 Wake       DarkWake to FullWake due to HID Activity: Using AC (Charge:100%)            718 secs  
03/03/13 15:12:21 GMT-03 Sleep      Clamshell Sleep to DarkWake: Using AC (Charge:100%)                         156 secs  
03/03/13 15:14:57 GMT-03 Wake       DarkWake to FullWake due to HID Activity: Using AC (Charge:100%)            834 secs  
03/03/13 15:28:51 GMT-03 Sleep      Clamshell Sleep to DarkWake: Using AC (Charge:100%)                         378 secs 
03/03/13 15:35:09 GMT-03 Wake       DarkWake to FullWake due to HID Activity: Using AC (Charge:100%)