Solve the equation $LaTeX: \displaystyle \log_{2}(x + 25)-\log_{2}(x - 3)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 25}{x - 3} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 25}{x - 3}=8$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 25=8 x - 24$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 7$ .