Solve the equation $LaTeX: \displaystyle \log_{2}(x + 44)-\log_{2}(x + 28)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 44}{x + 28} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 44}{x + 28}=2$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 44=2 x + 56$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -12$ .