Solve the equation $LaTeX: \displaystyle \log_{2}(x + 2)-\log_{2}(x - 2)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 2}{x - 2} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 2}{x - 2}=2$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 2=2 x - 4$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 6$ .