Question

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

Answer 1

Correct Answer - 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`