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wolframalpha.com states that $\log(0) = -\infty$
According to this QA as well as this website by the university of Minnesota $\log(0)$ is not defined. On the other hand, the definition on wikipedia states nothing about zero.
And a paper I am currently reading uses $\log(D)$ where $D \in \{0,1\}$.

So now, I'm confused as to which way is correct. Or does it depend on the context where one applies the log and both definitions ("undefined" and "$-\infty$") are common?

Bernard
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lucidbrot
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    The wiki states very clearly that $\log_b(a)$ is defined as a solution to $b^x=a$. Which is correct and no such solution exists for $b\neq 0$ and $a=0$. No, $\log(0)$ is not well defined. Sometimes people write $\log(0)=-\infty$ to denote that $\log(x)\to -\infty$ when $x\to 0$. – freakish Oct 16 '20 at 14:24
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    If an author explicitly defines the natural log function so that $\log(0) = -\infty$ then I'd say it's fine, as long as they're consistent. – littleO Oct 16 '20 at 14:29
  • @littleO So would it be reasonable for me to assume that the author means $log(0)=-\infty$ when they did not define it at all but do use it? In the end, I'm asking this question because I'm unsure whether I should question my understanding of the paper - it would make sense for minus infinity. – lucidbrot Oct 16 '20 at 14:37
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    Yes, I would guess that the author has defined their natural log function so that $\log(0) = -\infty$, and perhaps the author forgot to mention this. – littleO Oct 16 '20 at 14:44
  • @littleO Thank you for your help. I'm not too familiar with math.SE site culture - would you like to write your comments as an answer so that I can accept it? Or would that not be considered an answer because it's just "I'd say it's fine" and not based on sources? – lucidbrot Oct 16 '20 at 14:46
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    @lucidbrot I'll probably not post an answer in this case; feel free to either accept Wuestenfux's answer or post your own answer and accept it if you'd like. – littleO Oct 16 '20 at 18:44

1 Answers1

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Better $\lim_{x\rightarrow 0^+} \log(x) = -\infty$.

Wuestenfux
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