If $\ln x+\ln (x-4)=\ln (5 x)$, then $x=$

Step 1 ：First, we need to simplify the equation. According to the properties of logarithms, we can combine the left side of the equation to get \(\ln (x^2-4x)=\ln (5x)\).

Step 2 ：Next, we can remove the natural logarithm from both sides of the equation to get \(x^2-4x=5x\).

Step 3 ：Then, we rearrange the equation to get \(x^2-9x=0\).

Step 4 ：We can factor the equation to get \(x(x-9)=0\).

Step 5 ：Finally, we solve for x to get \(x=0\) or \(x=9\). However, since \(x\) cannot be 0 in the original equation, the only solution is \(x=\boxed{9}\).