Start with the equation \(\ln(1 + x) = 1 + \ln x\).

Use the property of logarithms: \(\ln a - \ln b = \ln \left( \frac{a}{b} \right)\).

Rearrange the equation: \(\ln(1 + x) - \ln x = 1\).

This becomes \(\ln \left( \frac{1 + x}{x} \right) = 1\).

Exponentiate both sides to remove the logarithm: \(\frac{1 + x}{x} = e\).

Rearrange to solve for \(x\): \(1 + x = ex\).

\(1 = ex - x\).

\(1 = x(e - 1)\).

\(x = \frac{1}{e - 1}\).

Calculate \(x\) using \(e \approx 2.718\):

\(x \approx \frac{1}{2.718 - 1} \approx 0.582\).

Round to 2 significant figures: \(x = 0.58\).