We can confirm that the Slim X2 and Slim X3 keyboards have the same size battery capacity. Here is the breakdown of their usage times, depending on what brightness level you set the backlight to:

Battery Life:

SLIM X2 BLUETOOTH BACKLIT KEYBOARD
ST-BTSX2M (battery: 1300mAh)

Level 1 - 9mA - 144h
Level 2 - 16mA - 81h
Level 3 - 27mA - 48h
Level 4 - 40mA - 32h
Level 5 - 53mA - 24h
Level 6 - 67mA - 19h
Level 7 - 82mA - 15h
Level 8 - 97mA - 13h
Level 9 - 113mA - 11h
Level 10 - 129mA - 10h

Backlit turns off if low battery - standby time is ~17 days when 15% battery capacity

Without backlight - Working time is 60 days total