Solve the equation $LaTeX: \displaystyle \log_{5}(x + 3105)-\log_{5}(x + 605)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 3105}{x + 605} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 3105}{x + 605}=5$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 3105=5 x + 3025$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 20$ .