若P={x|4x-10×2x+16<0},Q={x|log3x+log3(x-1)>log32},则P∩Q=( )
A.(3,+∞)
B.(-1,2)
C.(2,3)
D.(1,2)
P={x|4x-10×2x+16<0}={x|(2x-2)(2x-8)<0}={x|2<2x<8}={x|1<x<3},
Q={x|log3x+log3(x-1)>log32}={x|
}={x|x>2},x>0 x-1>0 x(x-1)>2
故P∩Q=(2,3),
故选C.
若P={x|4x-10×2x+16<0},Q={x|log3x+log3(x-1)>log32},则P∩Q=( )
A.(3,+∞)
B.(-1,2)
C.(2,3)
D.(1,2)
P={x|4x-10×2x+16<0}={x|(2x-2)(2x-8)<0}={x|2<2x<8}={x|1<x<3},
Q={x|log3x+log3(x-1)>log32}={x|
}={x|x>2},x>0 x-1>0 x(x-1)>2
故P∩Q=(2,3),
故选C.