Question

log2 (x²+x+1)+log, (x-1)=3, then x =
If​

Answer 1

Answer:

log

2

(3−x)+log

2

(1−x)=3 is defined for 3−x>0 and 1−x>0

⇒x<3 and x<1

∴ It is defined for x<1

log

2

(3−x)+log

2

(1−x)=log

2

2

3

=log

2

8

log

2

(3−x)(1−x)=log

2

8

Since, loga+logb=logab

(3−x)(1−x)=8

3−4x+x

2

=8

x

2

−4x−5=0

x

2

−5x+x−5=0

x=5,−1

But, x<1⇒x=−1

Only one root .