If $\ln x+\ln (x-7)=\ln (3 x)$, then $x=$ Next Question

Step 1 ：Given the equation in logarithmic form: \(\ln x+\ln (x-7)=\ln (3 x)\)

Step 2 ：Using the properties of logarithms, the sum of the logarithms of two numbers is equal to the logarithm of the product of those numbers.

Step 3 ：So, we can rewrite the left side of the equation as \(\ln(x*(x-7))\).

Step 4 ：Then, we equate it to the right side of the equation and solve for x.

Step 5 ：By solving the equation, we find that x = 10.

Step 6 ：Substituting x = 10 into the equation, we find that the equation holds true.

Step 7 ：Final Answer: The solution to the equation is \(\boxed{10}\).