已知函数y=loga(x+3)-1(a>0,且a≠1)的图象恒过定点A,若点A在直线mx+ny+1=0上,其中mn>0,则
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∵x=-2时,y=log21-1=-1,
∴函数y=log2(x+3)-1(a>0,a≠1)的图象恒过定点(-2,-1)即A(-2,-1),
∵点A在直线mx+ny+1=0上,
∴-2m-n+1=0,即2m+n=1,
∵mn>0,
∴m>0,n>0,
+1 m
=2 n
+2m+n m
=2+4m+2n n
+n m
+2≥4+2•4m n
=8,
•n m 4m n
当且仅当m=
,n=1 4
时取等号.1 2
故选D.