i ve just start playing civ iv
chopping down trees looks good in the short term, 30 free production
however you lose the 1 production per turn of the forest square
isnt it better in the longterm to keep the forest if your only considering production?????
You can't only consider production!

Chopping is almost always best for a few reasons:
-It provides a large short term benefit and during the early game, your cities can't get big enough to work many forests anyway. If you chop them they can contribute without being worked.
- Faster expansion by getting more workers and settlers earlier leading to more land, chopping these units is the only way to get the most out of the expansive and imperialistic traits.
-Getting wonders before an AI usually involves maximising all the production you can get in a short time, chopping is almost mandatory.
- Having a specific building complete fast really matters in a lot of cases, granaries allow more slave whipping, libraries allow scientist specialists and theres even a useful trick where you can make quite a lot of gold from overbuilding things
-Forests give enemy forces defensive bonuses making it very hard to stop them attacking cities, this alone is a good enough reason to chop all forests directly adjacent to a city.
-Tiles improved by workers with mines, cottages and later workshops, waterwheels etc are a
lot more productive than a forest, building over them is beneficial. The improvement to improve forests comes late and isn't much good either.
-Chopping with slave whipping is the fastest way to build an army early on and early war can win games often.
In short, early advantages in civ 4 snowball very quickly
There are some reasons to keep forests, primarily due to

. But I routinely chop 95% of any forests in my territory.