"It is quiet in the forest."
Translation:В лесу тихо.
Тихо в лесу should be considered as the correct answer also. It is also a first sentence in a famous song :)
This a rudiment of an old locative declension form. For most nouns, their locative form became identical to the prepositional form, so we usually do not distinguish them. Yet you can find a handful of old Russian words, for which the two forms are still different. With some of then, the locative form is disappearing as we speak. For example, you can still say "в дому", but "в доме" is equally acceptable. "В лесу", however, is the only acceptable form.
Mostly we say "в доме", not "в дому" though. Actually I can't remember when I heard someone speaking like that.
At least in my family it was not that uncommon - usually in the context of not having something at home: У нас в дому нет соли, нужно купить. In all other contexts "в доме" sounds more natural.
St. Petersburg. Although now that I think about it, this particular use may have originated form my grandmother who came from Arkhangelsk.
тихо в лесу
As others indicated, there is a [cutely obscene, if there is such a thing] song that schoolboys in Russia thing, in which each verse starts with the above line. E.g.,
тихо в лесу, только не спит барсук. знает барсук, что его [...] повесят на сук, вот и не спит барсук.
тихо в лесу, только не спит енот. знает енот, что его [...] рот, вот и не спит енот.