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Solve the equation log(x^(2)-6x+8)[log(2...

Solve the equation `log_(x^(2)-6x+8)[log_(2x^(2)-2x+8)(x^(2)+5x)]=0`

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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