已知: a n =lo g n+1 (n+2)(n∈ N * ) ,观察下列运算: a 1 ? a 2 =lo g 32 ?lo g 43 = lg3 lg2 ? lg4 lg3 =2 , a 1 ? a 2 ? a 3 ? a 4 ? a 5 ? a 6 =lo g 32 ?lo g 43 ?…?lo g 76 ?lo g 87 = lg3 lg2 ? lg4 lg3 ?…? lg7 lg6 ? lg8 lg7 =3 则当a 1 ?a 2 ?…?a k =2012时,自然数k为( )
A.
2 2012 +2
B.
2 2012
C.
2 2012 -2
D.
2 2012 -4
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