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)." \[ \log _{6}(x+1)-\log _{6}(x-3)=2 \] Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts

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 \(\boxed{\frac{109}{35}}\).