Part 2 of 2 Solve the logarithmic equation. \[ \log x+\log (x-9)=1 \] Determine the equation to be solved after removing the logarithm. \[ x \cdot(x-9)=10 \] (Type an equation. Do not simplify.) 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. Yype an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Step 1 ：\(\log x+\log (x-9)=1\)

Step 2 ：Using the properties of logarithms, rewrite the equation as \(\log [x \cdot (x-9)] = 1\)

Step 3 ：Rewrite the equation in exponential form to get \(x \cdot (x-9) = 10\)

Step 4 ：This is a quadratic equation, which can be written as \(x^2 - 9x - 10 = 0\)

Step 5 ：Factor the equation to get \((x - 10)(x + 1) = 0\)

Step 6 ：Setting each factor equal to zero gives the solutions x = 10 and x = -1

Step 7 ：Check these solutions in the original logarithmic equation

Step 8 ：Substituting x = 10 into the original equation, we get \(\log 10 + \log (10 - 9) = 1 + 0 = 1\), so x = 10 is a valid solution

Step 9 ：Substituting x = -1 into the original equation, we get \(\log (-1) + \log (-1 - 9)\), since the logarithm of a negative number is undefined, x = -1 is not a valid solution

Step 10 ：Therefore, the solution set is \(\boxed{10}\)