Solve the following logarithmic equation.
\[
\log _{8}(x+1)+\log _{8}(x-6)=1
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.)
B. There is no solution. The solution is empty set, $\varnothing$.

Step 1 ：Combine the two logarithms on the left side of the equation into one using the property of logarithms that states that the sum of two logarithms with the same base is the logarithm of the product of the numbers. This gives us a single logarithm on the left side of the equation: \(\log _{8}((x+1)(x-6))=1\).

Step 2 ：Convert the logarithmic equation into an exponential equation: \(8^{1} = (x+1)(x-6)\).

Step 3 ：Solve the equation for x: \(x^{2} - 5x - 6 = 8\).

Step 4 ：The solutions from the equation are x = -2 and x = 7.

Step 5 ：Check these solutions in the original equation because logarithms are undefined for negative numbers and zero. The valid solution is x = 7.

Step 6 ：Final Answer: The solution set is \(\boxed{7}\).