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Number of real values of x satisfying th...

Number of real values of x satisfying the equation `log_(x^2+6x+8)(log_(2x^2+2x+3)(x^2-2x))=0` is equal to

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`log_(x^(2)+6x+8)(log_(2x^(2)+2x+3)(x^(2)-2x))=0`
`therefore log_(2x^(2)+2x+3)(x^(2)-2x)=1`
`therefore x^(2)-2x=2x^(2)+2x+3`
`rArr x^(2)+4x+3=0`
`rArr (x+1)(x+3)=0`
`therefore x=-1,-3`
But for `x=-3,x^(2)+6x+8lt0`
`therefore x=-1`
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