I can't explain why others have voted the way they have. I haven't voted on this, I would not have voted on this, and I have no particular position on whether it should be closed or not.
Instead, I can offer some suggestions about how to improve the question or ask a better question, which might identify a path to re-opening the question.
State the problem clearly. Right now the problem is not stated clearly. It is not clear to me what the requirements are. We need the requirements to be stated clearly, so answerers can predict whether a candidate answer they have in mind will be satisfactory, and so voters will know how to vote.
Generally speaking, describing a problem by analogy is not ideal. The question has the format "here is a trick for computing exp, is there something like that for log?" I find it a little hard to extract requirements from that. It is often helpful to start by asking yourself, what approaches have I considered and rejected, and why have I rejected them? That often helps identify what the requirements are. Perhaps the requirement is some kind of computational efficiency? or some kind of numerical accuracy? or something else? Or perhaps the question is, given a subroutine to compute $\log x$ for any $0 \le x \le 1$, is there a simple way to compute $\log x$ for all $x$? And if so, what counts as simple? What is wrong with ignoring the subroutine and computing the log directly using any of the standard algorithms to compute the log? I find it hard to tell.
Ultimately, I'm forced to guess what the individual has in mind.
Do research before asking. It is often very helpful to do a significant amount of research before asking, and try to solve the problem yourself, and look for existing solutions. Often, this process enables you to answer your question on your own. Or, if you still don't know how to solve the problem, often it helps clarify the problem statement and helps write a question that will be relevant and useful to others and provide context and background that helps situation your question in the broader scheme of things.
It's not clear to me what research the poster has done. There is lots written on how to compute the log in floating point arithmetic, and I believe it is documented in standard resources. What is wrong with all those standard methods? Is there some specific shortcoming they suffer? Or is the poster just unaware and wanting someone else to do that research for them or hoping someone else who already knows all that will share their knowledge with them?
In my view, an important part of our mission is to build an archive of knowledge that will be useful to others. Think of each question as like an encyclopedia article, except we have replaced a topic heading with a question. In my view, we want a question where it's clear what the request is, and where it will lead to answers that add to the knowledge available on the Internet. A question that asks us to repeat information that is already found in standard resources might not be contributing to this archive of knowledge.
When someone figures out an answer to their own question by asking ChatGPT, and then posts it as an answer, but they don't indicate whether this is a satisfactory solution or not, or they are unable to tell for themselves whether it is satisfactory -- that is a potential warning sign. It potentially indicates a lack of research, and a question that might not be adding new knowledge to the Internet. It also potentially indicates a lack of clarity about the requirements if the poster is unsure about their solution. Alternatively, if they recognize it as a valid solution, it should have been posted as an answer, not a comment. So seeing this raises some questions about which of these cases the situation falls into, and might make some people concerned about lack of clarity in the requirements and concerned it might be a chameleon question.
Not everyone agrees with my view about the purposes of Stack Exchange or Math.SE -- indeed, a large fraction of the community (perhaps even the majority) probably has a different view. But perhaps this gives you some possible hypotheses about thinking that might have been behind some of the votes. I'm just speculating, but perhaps some of the voters came from a similar mindset and had concerns of this sort.
I don't know why others have voted as they have, but if you'd like it to be re-opened, perhaps these identify a possible path to re-opening -- some ways to address potential concerns that might be influencing voters.
That said, this is a tricky case, because improving the question to address these limitations might require substantial edits, and Math.SE culture is... wary (at best) of substantial edits by anyone other than the original poster. So it's possible that the only way for anyone other than the original poster to solve these problems is by asking a new question yourself, a new question that is better formulated and addresses these shortcomings, and then linking the old question to the new one.
