Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (ø)."
\[
\log _{6}(x+1)-\log _{6}(x-3)=2
\]
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Final Answer: The solution to the equation is \(\boxed{\frac{109}{35}}\).
Step 1 ：Define the variable x.
Step 2 ：Define the equation \(\log _{6}(x+1)-\log _{6}(x-3)=2\).
Step 3 ：Solve the equation to get \(x = \frac{109}{35}\).
Step 4 ：Check if the solution is valid. The solution is valid if \(x > 3\).
Step 5 ：The solution \(x = \frac{109}{35}\) is valid because it is greater than 3, which makes the arguments of the logarithms in the original equation positive.
Step 6 ：Final Answer: The solution to the equation is \(\boxed{\frac{109}{35}}\).
