Deforestation in Amazon down 83% since peak in 2004.

[Bill USA]

Since Brazil started enforcing laws against illegal logging and other activities which destroy rainforests they have made considerable progress in reducing deforestation. In 2004 10,722 sq.miles of forest were lost. In 2012, 1,800 sq. miles were lost.

According to Mongabay the biggest factor in deforestation is the expansion of pastureland for cattle.



http://www.mongabay.com/brazil.html
(emphasis my own)

A Closer Look at Brazilian Deforestation (Update: Future threats to the Amazon)

Like other places in the tropics, deforestation in Brazil is increasingly the result of urban consumption and trade rather than subsistence agriculture.

Today deforestation in the Amazon is the result of several activities, the foremost of which include:
Clearing for cattle pasture
Colonization and subsequent subsistence agriculture
Infrastructure improvements
Commercial agriculture
Logging

Clearing for Cattle Pasture
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Cattle ranching is the leading cause of deforestation in the Brazilian Amazon. This has been the case since at least the 1970s: government figures attributed 38 percent of deforestation from 1966-1975 to large-scale cattle ranching. Today the figure is closer to 60 percent, according to research by Brazil's National Institute for Space Research (INPE) and its Agricultural Research Corporation (Embrapa). Most of the beef is destined for urban markets, whereas leather and other cattle products are primarily for export markets.

Brazil is today the world's largest exporter and producer of beef. Much of its expansion has taken place in the Amazon, which currently has more than 80 million head of cattle, up from 26.6 million in 1990 and equivalent to more than 85 percent of the total U.S. herd. The Brazilian Amazon has more than 214,000 square miles of pasture, an open space larger than France.
(more)