1. Problem: Find the zeros of the function $$f(x) = \frac{(\ln x)^2}{2 - x}$$. 2. To find zeros of a function, set the numerator equal to zero and ensure the denominator is not zero. 3. The numerator is $$(\ln x)^2$$. Set it equal to zero: $$ (\ln x)^2 = 0 $$ 4. Taking the square root of both sides: $$ \sqrt{(\ln x)^2} = \sqrt{0} \implies |\ln x| = 0 $$ 5. This implies: $$ \ln x = 0 $$ 6. Recall that $\ln x = 0$ when: $$ x = e^0 = 1 $$ 7. Check the denominator at $x=1$: $$ 2 - 1 = 1 \neq 0 $$ 8. Since denominator is not zero, $x=1$ is a zero of the function. 9. Domain considerations: $x > 0$ because $\ln x$ is defined only for positive $x$. 10. Final answer: $$ \boxed{1} $$ is the zero of the function.