Question

Solve:
$\log (x+2)+\log (x-2)=\log 5$

Answer 1

A] $log(x+2)+log(x-2)=log5$

as $lo{g}^a+lo{g}^b=lo{g}^{ab}$

$\Rightarrow log\left(\right(x+2\left)\right(x-2\left)\right)=log5$

$\Rightarrow x^2-2^2=5$

$\Rightarrow x^2=5+2^2$

$\Rightarrow x^2=5+4=9$

$x=\pm 3$

as x cant be -ve

$\therefore x=3$