$sqrtn$ vs $5^log_2n$ [closed]

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I have this problem.




Given $f(n) = sqrtn$ and $g(n) = 5^log_2n$, which one is faster?



  1. $f(n) = mathcal O(g(n))$

  2. $g(n) = mathcal O(f(n))$

  3. Both



I solved a couple of exercises, but the problem with this one is that I don't have any idea how to compare these two!




algorithms logarithms asymptotics




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closed as off-topic by Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon Aug 25 at 10:38


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.












  • @dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
    – Did
    Aug 25 at 5:51














up vote
-3
down vote

favorite












I have this problem.




Given $f(n) = sqrtn$ and $g(n) = 5^log_2n$, which one is faster?



  1. $f(n) = mathcal O(g(n))$

  2. $g(n) = mathcal O(f(n))$

  3. Both



I solved a couple of exercises, but the problem with this one is that I don't have any idea how to compare these two!




algorithms logarithms asymptotics




share|cite|improve this question














closed as off-topic by Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon Aug 25 at 10:38


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.












  • @dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
    – Did
    Aug 25 at 5:51












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I have this problem.




Given $f(n) = sqrtn$ and $g(n) = 5^log_2n$, which one is faster?



  1. $f(n) = mathcal O(g(n))$

  2. $g(n) = mathcal O(f(n))$

  3. Both



I solved a couple of exercises, but the problem with this one is that I don't have any idea how to compare these two!




algorithms logarithms asymptotics




share|cite|improve this question














I have this problem.




Given $f(n) = sqrtn$ and $g(n) = 5^log_2n$, which one is faster?



  1. $f(n) = mathcal O(g(n))$

  2. $g(n) = mathcal O(f(n))$

  3. Both



I solved a couple of exercises, but the problem with this one is that I don't have any idea how to compare these two!





algorithms logarithms asymptotics





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 25 at 6:23









an4s

2,0632417




2,0632417










asked Aug 25 at 5:42









Yousef Alghofaili

81




81




closed as off-topic by Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon Aug 25 at 10:38


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon Aug 25 at 10:38


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Jendrik Stelzner, Brahadeesh, user91500, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.











  • @dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
    – Did
    Aug 25 at 5:51
















  • @dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
    – Did
    Aug 25 at 5:51















@dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
– Did
Aug 25 at 5:51




@dxiv The OP is asking whether $sqrt n=o(5^log_2n)$ or the opposite.
– Did
Aug 25 at 5:51










1 Answer
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The trick is noticing that $5^log_2 x=5^fracln xln 2=e^fracln 5ln 2ln x=x^fracln 5ln 2$. And now it's all a matter of deciding which one is the largest between $log_25$ and $frac12$.






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote



    accepted










    The trick is noticing that $5^log_2 x=5^fracln xln 2=e^fracln 5ln 2ln x=x^fracln 5ln 2$. And now it's all a matter of deciding which one is the largest between $log_25$ and $frac12$.






    share|cite|improve this answer
























      up vote
      2
      down vote



      accepted










      The trick is noticing that $5^log_2 x=5^fracln xln 2=e^fracln 5ln 2ln x=x^fracln 5ln 2$. And now it's all a matter of deciding which one is the largest between $log_25$ and $frac12$.






      share|cite|improve this answer






















        up vote
        2
        down vote



        accepted







        up vote
        2
        down vote



        accepted






        The trick is noticing that $5^log_2 x=5^fracln xln 2=e^fracln 5ln 2ln x=x^fracln 5ln 2$. And now it's all a matter of deciding which one is the largest between $log_25$ and $frac12$.






        share|cite|improve this answer












        The trick is noticing that $5^log_2 x=5^fracln xln 2=e^fracln 5ln 2ln x=x^fracln 5ln 2$. And now it's all a matter of deciding which one is the largest between $log_25$ and $frac12$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 25 at 6:07









        Saucy O'Path

        3,531424




        3,531424












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