Question

If $\log (x+1)+\log (x-1)=\log 3$, then the value of $x$ will be

• A. $3$
• B. $2$
• C. $1$
• D. None of these

Answer 1

The correct option is B $2$

Given:

$\log (x+1)+\log (x-1)=\log 3$

$⟹\log (x+1)(x-1)=\log 3$

Using multiplication rule of logarithms,

$\log a+\log b=\log ab$

Thus, $\log (x^2-1)=\log 3$

$⟹\Rightarrow x^2-1=3$

$⟹\Rightarrow x=\pm 2$

But $x\ne -2\because x-1>0\Rightarrow x>1$

$\therefore x=2$

Hence, option C.