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Is this question proper? "Solve $\log_{10}x\in\mathbb{R}$."?

I know that $\log_{10}x\in\mathbb{R}$ means $x\in(0,\infty)$, but can we write "Solve $\log_{10}x\in\mathbb{R}$." as a question alone? Thank you.

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What are you trying to solve? What would the correct answer be? – Joel Cornett Oct 21 '12 at 3:57
Rather than "solve", maybe you could write "Find all x such that $\log _{10}x \in R$" – The Chaz 2.0 Oct 21 '12 at 3:58
up vote 2 down vote accepted

Perhaps it would be better to ask, "For what $x$ is $\log_{10} x \in \mathbb{R}$?" When you say "solve" it suggests there are a finite number of solutions, and there aren't finitely many.

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But "Solve $x+1>0$", which has finitely many solutions, is a proper question... – ᴊ ᴀ s ᴏ ɴ Oct 21 '12 at 4:02
Hm, first, do you mean "infinitely" many? This is fairly subjective, I suppose, but I wouldn't use the phrase "Solve." What resonates better for me is: "For what $x$ is $x+1 > 0$?" Alternately if you go with what BobaFret says, "Solve $x+1>0$." makes sense because you are simplifying the inequality and isolating $x$ to one side, thereby getting information about $x$ itself. – Michael Zhao Oct 21 '12 at 16:09
Yes, I mean "infinitely". – ᴊ ᴀ s ᴏ ɴ Oct 22 '12 at 7:58

"Solve $\log_{10}x$" may make sense if you interpret "solve" as evaluate/simplify. For example: "Solve $\log_{10}100$":


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