The equation \[ \ln (x+1)-\ln (x)=2 \] has the solution $x=$ Hint: First use the properties of logarithms, then apply the exponential on both sides.

Step 1 ：Rewrite the equation using the properties of logarithms: \(\ln\left(\frac{x+1}{x}\right) = 2\)

Step 2 ：Apply the exponential on both sides to get rid of the logarithm: \(\frac{x+1}{x} = e^2\)

Step 3 ：Solve the equation for x: \(x = \frac{1}{e^2 - 1}\)

Step 4 ：Final Answer: \(x = \boxed{\frac{1}{e^2 - 1}}\)