Solve the following logarithmic equation.
\[
\log (6 x+5)-\log (x-4)=1
\]

Select the correct choice below and, if necessary, fill in the answer box.
A. The solution is $x=\square$.
(Type an integer or a simplified fraction.)
B. The solution is not a real number.

Step 1 ：Solve the equation \(\frac{6x+5}{x-4} = 10\) for x by first multiplying both sides of the equation by \(x-4\) to get rid of the denominator on the left side. This gives us \(6x+5 = 10(x-4)\).

Step 2 ：Distribute the 10 on the right side to get \(6x+5 = 10x - 40\).

Step 3 ：Solve for x by subtracting 6x from both sides and adding 40 to both sides. This gives us \(x = \frac{45}{4}\).

Step 4 ：Check if this solution is valid. The original equation has a logarithm of \(x-4\), so \(x-4\) must be greater than 0. This means that \(x\) must be greater than 4. Since \(\frac{45}{4}\) is greater than 4, the solution is valid.

Step 5 ：The solution is \(x = \boxed{\frac{45}{4}}\).