Title: $x^x(\ln(x)+1)=b$
Body: I want to solve for $x$ and have tried solving it myself and used many algebraic calculators including wolfram alpha, and I could not get any answer from anything. If you can solve it please show me how, and if it is impossible please explain why to me. Thank you.

Please tell me what tag to put on my question, I am having considerable trouble.

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A general advice on choice of tags: How am I supposed to use tags?

I will repeat one advice given there - during and after posting the question you're shown several lists of similar questions. You could check some of those post, maybe looking at the tag used on other related posts will help you to find some other suitable tag.

You could also try asking in the tagging chatroom for some advice - admittedly, this room is not very active, but at least a few users do visit that room occasionally.

Also keep in mind that there are many users around who try to improve how questions are tagged - so if somebody notices your question and has an idea for better tags, they might simply edit the tags or leave a comment with suggestions for the choice of tags. (And from those edits you might learn about some tags which are available on the site and which might be useful in the future.)

Another thing to keep that in some cases we only notice that some tag is relevant for the question after an answer is posted. See: Retagging after an answer is given.

For this specific question I thought about these tags, some of them might probably suitable (choice is up to you - I am aware that there are only five slots for tags, I have mentioned several which are possible candidates):

  • - since the question is about symbolic manipulation with variables, which falls (broadly) under algebra.
  • - simply because the question is about a transcendental equation.
  • and - since those are the operations which appear in your question.
  • Choice of other tags might depend on what you actually want to achieve. If you want to get a solution in closed form (and ask whether finding closed form is actually possible), you might choose . If approximating the solution is sufficient for you, you might want or some of the related tags.
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