Question

If \(2 \log (x+1)-\log \left(x^{2}-1\right)=\log 2\), then \(x=\)
(A) only 3
(B) \(-1\) and 3
(C) only-1
(D) 1 and 3

Answer 1

Ans : (A)
Hint \(: \log \left\{\frac{(x+1)^{2}}{x^{2}-1}\right\}=\log 2 \Rightarrow(x+1)^{2}=2\left(x^{2}-1\right) \Rightarrow x^{2}-2 x-3=0 \Rightarrow(x-3)(x+1)=0\)
$$
x=3 ; x \neq-1
$$