1. The problem is to understand the value of $\log(\infty)$. 2. By definition, $\log(x)$ is the inverse function of the exponential function, so $y = \log(x)$ means $x = e^y$ (assuming natural logarithm). 3. As $x \to \infty$, we want to see what happens to $\log(x)$. 4. The logarithmic function grows without bound but at a slower rate than any power of $x$. 5. Therefore, as $x \to \infty$, $\log(x) \to \infty$. 6. Hence, $\log(\infty) = \infty$ (it diverges to infinity). Final answer: $\log(\infty) = \infty$