Question

Solve log.(x² + x) - log, (x + 1) = 2.
​

Answer 1

Answer:

log

x+1

(x

2

+x−6)

2

=4

(x+1)

4

=(x

2

+x−6)

2

⇒2x

3

+17x

2

+16x−35=0

⇒(x−1)(2x

2

+19x+35)=0

⇒(x−1)(2x+5)(x+7)=0

⇒x=1,−7,−

2

5

Now, from the given equation it follows that

x+1>0,x+1



=1,x

2

+x−6



=0

x>−1,x



=0,x



=−3,x



=2

⇒x∈(−1,0)∪(0,2)∪(2,∞)

So,x=1 lies in this range.

So, required value =2

Step-by-step explanation:

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Answer 2

Answer:

x=100

Step-by-step explanation:

log.(x² + x) - log, (x + 1) =2

2=log(x²+x/x+1)

logx=2

x=10²

x=100