Solve the equation $LaTeX: \displaystyle \log_{4}(x + 253)-\log_{4}(x + 61)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{4}\frac{x + 253}{x + 61} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 4$ gives $LaTeX: \displaystyle \frac{x + 253}{x + 61}=4$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 253=4 x + 244$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 3$ .