1. **State the problem:** Solve the inequality $-2\ln(x-1) < 0$. 2. **Recall the properties:** The natural logarithm function $\ln(y)$ is defined for $y > 0$. 3. **Rewrite the inequality:** Divide both sides by $-2$ (note that dividing by a negative number reverses the inequality): $$-2\ln(x-1) < 0 \implies \ln(x-1) > 0$$ 4. **Interpret the inequality:** $\ln(x-1) > 0$ means that the argument $x-1$ is greater than 1 because $\ln(a) > 0$ if and only if $a > 1$. 5. **Solve for $x$:** $$x - 1 > 1 \implies x > 2$$ 6. **Domain check:** Since $\ln(x-1)$ is defined only for $x-1 > 0$, we have $x > 1$. The solution $x > 2$ satisfies this domain. **Final answer:** $$x > 2$$