Solve the following logarithmic equation.
\[
\log (7 x+9)=1+\log (x-1)
\]

Select the correct choice below and, if necessary, fill in the answer box to comp
A. The solution set is \{\} .
(Simplify your answer. Type an exact answer. Use a comma to separate
B. There is no solution.

Step 1 ：\(\log (7 x+9) - 1 = \log (x-1)\)

Step 2 ：\(\log (7 x+9) - \log 10 = \log (x-1)\)

Step 3 ：\(\log \left(\frac{7x+9}{10}\right) = \log (x-1)\)

Step 4 ：\(\frac{7x+9}{10} = x-1\)

Step 5 ：\(7x + 9 = 10x - 10\)

Step 6 ：\(9 = 3x - 10\)

Step 7 ：\(19 = 3x\)

Step 8 ：\(x = \frac{19}{3}\)

Step 9 ：Check: \(\log (7 \cdot \frac{19}{3} + 9) = 1 + \log (\frac{19}{3} - 1)\)

Step 10 ：Check: \(\log (44) = 1 + \log (5)\)

Step 11 ：\(\boxed{\text{No Solution}}\)