how do I clear the phone log on my gear

Go into the phone application on your Samsung device
Tap on Logs
To delete a single log: Tap and hold on the individual call, select Delete from the popup box, and then tap on Delete to confirm
To clear multiple items: Press the Menu key to the left of the home button, select Delete, select one or all of the logs you wish to delete, and tap Delete in the upper right of the screen to perform the action
Those items will no longer show on your Galaxy Gear
Then
Go into the phone application on your Samsung device
Tap on Logs
Press the Menu key
Choose View and change the option from All calls to All Logs
Press the Menu key again and select Delete
Tap on Select all and then Delete to clear all the items in the list
Go into the Logs app on your Gear and the list should now be empty