Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (Ø)." \[ \ln (x+3)-\ln (x)=1 \]

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

Step 2 ：Using the properties of logarithms, the difference of two logarithms with the same base is the logarithm of the quotient of the numbers. So, we can rewrite the equation as \(\ln \left(\frac{x+3}{x}\right) = 1\).

Step 3 ：Then, we can use the property of logarithms that says if \(\ln a = b\), then \(a = e^b\). So, we can rewrite the equation as \(\frac{x+3}{x} = e^1\).

Step 4 ：Solving this equation for \(x\), we get \(x = \frac{3}{e-1}\).

Step 5 ：However, we need to check if this solution is valid. A solution is invalid if it makes the argument of the logarithm non-positive. So, we need to check if \(x+3 > 0\) and \(x > 0\).

Step 6 ：The solution is valid, and simplifying it gives us \(x = 1.7459\).

Step 7 ：\(\boxed{x = 1.7459}\) is the solution to the equation.