1. **State the problem:** Solve the equation $x \times \ln(x) = 0$ for $x$. 2. **Recall the zero product property:** If a product of two factors equals zero, then at least one of the factors must be zero. So, either $$x = 0$$ or $$\ln(x) = 0$$ 3. **Analyze each factor:** - For $x = 0$, note that $\ln(x)$ is undefined for $x \leq 0$, so $x=0$ is not in the domain. - For $\ln(x) = 0$, recall that $\ln(x) = 0$ when $x = 1$ because $\ln(1) = 0$. 4. **Conclusion:** The only solution in the domain of the function is $$x = 1$$. Therefore, the solution to the equation $x \times \ln(x) = 0$ is $x = 1$.