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 $\frac{109}{35}$ .

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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 $\frac{109}{35}$ .

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