Question

Solve for $x$.
$\log \left(x+2\right)+\log \left(x-2\right)=\log 3+3\log 4$

Answer 1

$\log (x+2)+\log (x-2)=\log 3+3\log 4$

From the property $\log (x\times y)=\log x+\log y$

$\log \left[\right(x+2\left)\right(x-2\left)\right]=\log [3\times 4^3]$

Dropping $\log$ both side,

$x^2-4=192$

$x^2=196$

$x=14.$