Question

log4 (x2 +x)- log4 (x + 1) = 2
​

Answer 1

Answer:

x

2

+x>0 and x+1>0

⇒x(x+1)>0⇒x ∈ (−∞, −1)∪(0, ∞)

And x+1>0⇒x∈(−1, ∞)

Taking intersection, we have

⇒x∈(0, ∞)

Now,

log

4

(x

2

+x)−log

4

(x+1)=2

⇒log

4

(

x+1

x

2

+x

)[∵loga−logb=log

b

a

]=2

⇒

x+1

x(x+1)

=4

2

=16

⇒x=16