[tex]\dfrac{\lg x}{\lg (x+2)} = \dfrac{1}{2}\, \Leftrightarrow \, \log_{x+2}x = \dfrac{1}{2}\, \Leftrightarrow \,\log_{x+2}x = \log_{4} 2\\ \\\\\Rightarrow \boxed{x = 2}[/tex]
