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Find the number of positive integers such that logarithm of whose reciprocals to the base 10 has the characteristic $-2$.


Let $x$ be a positive integer.
Now the characteristic of $\log_{10}(\frac{1}{x})$ is $-2$
I dont know how to solve further.How to count number of positive integers?Please help me.Thanks.

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    $\begingroup$ I don't think you have the right definition of characteristic. You need a floor or ceiling function somewhere. $\endgroup$ – Ted Nov 30 '15 at 3:03
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If that is your question, $log_{10} {1/x} = -2$

${1/x} = 10^{-2}$

$x = 100$

does this help?

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  • $\begingroup$ No,this is not the answer.The answer is $90.$ $\endgroup$ – Vinod Kumar Punia Nov 30 '15 at 2:34
  • $\begingroup$ @Vinod, can u explain how u got the answer. $\endgroup$ – NiroshaR Nov 30 '15 at 2:35
  • $\begingroup$ I have just quoted the book's answer,i dont know how it came. $\endgroup$ – Vinod Kumar Punia Nov 30 '15 at 2:38
  • $\begingroup$ @vinod does the book meant number of such positive integers is $90$ $\endgroup$ – Ekaveera Kumar Sharma Nov 30 '15 at 6:35
  • $\begingroup$ Yes,number of such positive integers is $90$,@EkaveeraKumarSharma $\endgroup$ – Vinod Kumar Punia Nov 30 '15 at 6:40

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