Solve for x : (x - 2) + (x + 2) = 5 - Vidyadip

Question

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

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Answer

$\log (x-2)+\log (x+2)=\log 5$
$\Rightarrow \log (x-2)(x+2)=\log 5 \ldots\left[\log _a m+\log _a n=\log _a m n\right]$
$ \Rightarrow \log \left(x^2-4\right)=\log 5$
$ \Rightarrow x^2-4=5$
$ \Rightarrow x^2=9$
$ \Rightarrow x= \pm \sqrt{9}$
$ \Rightarrow x= \pm \sqrt{3^2}$
$ \Rightarrow x= \pm 3$

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