Question

If $2\log (x+1)-\log (x^2-1)=\log 2,$ then $x=$

• A. only $3$
• B. $-1$ and $3$
• C. only $-1$
• D. $1$ and $3$

Answer 1

The correct option is A only $3$

$\log (x+1{)}^2-\log (x^2-1)=\log 2\log \left|\frac{(x+1{)}^2}{(x^2-1)}\right|=\log 2\Rightarrow \frac{x+1}{x-1}=2\Rightarrow x+1=2x-2\Rightarrow x=3$