[tex] log_{2}(2x + 6) - log_{2}(x) = 3 \\ \Leftrightarrow log_{2}(2x + 6) = log_{2}(x) + 3 \times 1 \\ \Leftrightarrow log_{2}(2x + 6) = log_{2}(x) + 3 log_{2}(2) \\ \Leftrightarrow log_{2}(2x + 6) = log_{2}(x) + log_{2}(8) \\ \Leftrightarrow log_{2}(2x + 6) = log_{2}(8x) \\ \Leftrightarrow 2x + 6 = 8x\Leftrightarrow 6x = 6\Leftrightarrow x = 1[/tex]
