Question

If $\log (x-2)+\log (x+2)=\log 5$, then the value of $x$ is

• A. $2$
• B. $5$
• C. $1$
• D. $3$

Answer 1

The correct option is D $3$

$\log (x-2)+\log (x+2)=\log 5$
$\therefore \log (x-2)(x+2)=\log 5$....($\log a.b=\log a+\log b$)
$\therefore x^2-4=5$
$\therefore x^2-9=0$
$\therefore x=\pm 3$
Since $x>2$, x will be equal to $3$