chasv77answered grow question 5 years ago If the carbon filter is a good one, you could vent the exhaust right out into the larger room area. Trying to get it outside if not near a window is a trick, unless you have an unused dryer vent. Mount the exhaust on an upper corner, as heat rises, and it will be easier for it to vent out.
You should also get another 4" fan for internal circulation, and place cattycorner to your exhaust fan, near the bottom of the tent.