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.

Answer

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Answer

Final Answer: $x = \frac{1}{e^{2} - 1}$

Steps

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

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: $x = \frac{1}{e^{2} - 1}$