Solve the following logarithmic equation. \[ \log _{2}(5 x-3)-\log _{2}(3 x-1)=2 \] Write the equation obtained after applying the definition of and the properties of logarithms. (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Step 1 ：The given equation is a logarithmic equation with base 2. The properties of logarithms state that the difference of two logarithms is equal to the logarithm of the quotient of their arguments. Therefore, we can combine the two logarithms on the left side of the equation into a single logarithm. The equation then becomes: \[\log _{2}\left(\frac{5x-3}{3x-1}\right) = 2\]

Step 2 ：Next, we can apply the definition of logarithms to rewrite the equation in exponential form. The base of the logarithm becomes the base of the exponent, the right side of the equation becomes the exponent, and the argument of the logarithm becomes the result. This gives us: \[\frac{5x-3}{3x-1} = 2^2\]

Step 3 ：Finally, we can simplify the right side of the equation to get: \[\frac{5x-3}{3x-1} = 4\]

Step 4 ：Solving the equation gives us the solution: \[x = \frac{1}{7}\]

Step 5 ：Final Answer: The solution to the equation is \(\boxed{\frac{1}{7}}\)