I realized that I didn't provide sufficient information when I first posted my question and started editing it a few minutes after posting since I got the first downvote. I tried to provide as much as I could information and context in my edit (according to my level of knowledge of the topic) and submitted my edit within a few hours, but my question was not considered to re-open. Since I didn't receive any feedback on what is the issue, I'm now not sure how can I improve the phrasing of my question (problem), or is it considered just too basic to be answered here (if this is a thing!)?
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2$\begingroup$ Looking at the Question in its present state, I wonder if your interest is in approximating the logarithm with a first degree polynomial. Rewriting suggests an exact formula, which won't exist, but perhaps you want an approximation over a certain range with a specified accuracy? Those would be concrete details to fill in, and could relate to earlier Questions already answered. $\endgroup$– hardmathCommented Aug 4 at 13:13
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$\begingroup$ @hardmath thank you this is helpful $\endgroup$– Es_aCommented Aug 5 at 20:27
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$\begingroup$ Summary of math.stackexchange.com/posts/4952492/timeline – Question was closed 30 July, reopened 3 August, closed again 6 August, deleted 6 August. $\endgroup$– Gerry MyersonCommented Aug 6 at 22:51
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2 Answers
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I have left you some comments on the question. Please revise the question to address all of the feedback.
Note that part of our mission is to build an archive of knowledge that will be useful to others in the future. We're not just a help desk to solve your math problems for you -- we are a site where people can collaborate to build up this library of information (in the form of questions and answers). So people are more likely to be enthusiastic about questions that seem likely to be useful to others in the future, and are clearly expressed. Your question seems very specific to your specific situation and it seems unlikely that anyone else will have exactly the same question, so this might diminish enthusiasm for your question. Also it is a little confusing what you are asking, which might also diminish enthusiasm.
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$\begingroup$ Thank you for your comments, I revised the question to address the feedback. My question was closed again after this revision and I'm not looking for discussing re-opening anymore. I do really appreciate all the comments, especially the two other users who mentioned approximation and tangent which helped me advance my understanding of the issue. $\endgroup$– Es_aCommented Aug 5 at 20:28
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$\begingroup$ I also appreciate you taking the time reflecting on the mission of building an archive of knowledge to be useful for others in the future. It's a great mission that I'm happy I joined. There is also nothing wrong with asking for help or helping people in the present while building such an archive. Every one has a timeline growing and learning, and giving a feedback and a genuine chance to edit when the code is respected is necessary and appreciated. Especially for new comers or people from across discipline, which can help stimulate and exchange ideas at worst. $\endgroup$– Es_aCommented Aug 5 at 20:33
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1$\begingroup$ As of the statement that my question "seems unlikely that anyone else will have exactly the same question", I find such judgment to be inaccurate and controversial in many ways, but I take your point about enthusiasm! Again, thank you for the comments and the discussion! you may close this question too if you see it appropriate $\endgroup$– Es_aCommented Aug 5 at 20:34
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I am one of those who downvoted/voted-to-close. It is nothing personal, but the question even in edited form, has problems. I have to stick with my votes.
What do you mean that the linear approximation to $\ln(a - x)$ in terms of $\ln a$ and $x$ is "close to" the precise value of $\ln(a-x)$. How close do you need? This made me hit the "Needs details/clarity" button.
Surely you could've tried some relevant values of $x$ to start. What happens when $x = o(a)$? Or $x = \theta(a)$, say $x=\frac{a}{4}$ or $x=\frac{a}{2}$. These aren't just insights for you but these are also observations that I feel should be in your question. This omission in light of 1. above makes me think the question was not thought out as it should be.
Both 1. and 2. put together are quite problematic for a question I must say!
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$\begingroup$ 1. well taken. I addressed this in the latest edit by using the approximation error. 2. is valid, probably to any question! I appreciate the comments, thanks. This question is deleted now $\endgroup$– Es_aCommented Aug 7 at 13:08