$\log(0)$ is $-\infty$, but $\log(0)=x$ is undefined

Question

In Wolfram Alpha, $log(0)$ results in $-\infty$. However, $log(0)=x$ results in undefined.

Link to $\log(0)$ : Wolfram Alpha

Link to $\log(0)=x$ : Wolfram Alpha

Shouldn't these result in the same answer?

Answer 1

The equation $\log(0)= -\infty$ is misleading. Actually $\log(0)$ is undefined. What is true is that $\lim_{x \to 0+} \log(x) = -\infty$.