$\log m + \log n = \log mn$
So, $\log x + \log (x-7) = \log (x+11) + \log 2$
$\Rightarrow \log x(x-7) = \log 2 (x+11)$
$\Rightarrow x(x-7) = 2 (x+11)$
$\Rightarrow x^2-9x-22=0$
$\Rightarrow (x-11)(x+2)=0$
$\therefore x=11$
$\because x \neq -2$ , log is undefined for negative number.