Solve the equation $LaTeX: \displaystyle \log_{2}(x + 14)-\log_{2}(x + 6)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 14}{x + 6} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 14}{x + 6}=2$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 14=2 x + 12$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 2$ .