Question

log4 x^2+1/(x-1)^2=log4 |4-x|

Answer 1

log

4

(x

2

−1)−log

4

(x−1)

2

=log

4

(4−x)

2

⇒log

4

(x−1)

2

(x

2

−1)

=log

4

(4−x)

2

⇒

(x−1)

2

x

2

−1

=4−xorx−4.

Firststep

x−1

x+1

=4−x,x



=1

⇒x+1=−x

2

+5x−4

⇒−x

2

+4x−5=0

⇒x

2

−4x+5=0

Nosolution.

SecondStep.

x−1

x+1

=x−4

⇒x+1=x

2

−5x+4

⇒x

2

−6x+3=0

⇒x=3±

6

.

Butx



=3−

6

.

Therefore,x

2

−1<0atx=3−

6

Therefore,x=3+

6

isonlysolution.