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

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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












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
1






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



























    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












            -

            這個網誌中的熱門文章

            Is there any way to eliminate the singular point to solve this integral by hand or by approximations?

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite 1 $$int_0^1 (1+(x^-p-1)^1-p)^frac1pdx, pin mathbbR, pge 1$$ I find that $x=0,1$ are singular points(discontinuous points of this integral), is there a way to eliminate those singular points to make sure that this integral can be calculated by hand or by Taylor approximations. In either cases, what are those steps of calculating the integral? calculus real-analysis analysis approximation share | cite | improve this question edited Sep 11 at 5:07 asked Sep 11 at 4:48 Mclalalala 126 8 1 What is $p$? Please give more information to make it complete. – xbh Sep 11 at 5:02 @xbh already fixed it, thanks for reminding. – Mclalalala Sep 11 at 5:10 Seems that $0$ is not singular here… [I might compute wrong] – xbh Sep 11 at 5:30 @xbh can you show me how to get the close formula for the integral above? – Mclalalala Sep 11 at 5:33
            閱讀完整內容

            Why am i infinitely getting the same tweet with the Twitter Search API?

            圖片
            up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia
            閱讀完整內容

            Carbon dioxide

            圖片
            "CO2" redirects here. For other uses, see CO2 (disambiguation). Carbon dioxide Names Other names Carbonic acid gas Carbonic anhydride Carbonic oxide Carbon oxide Carbon(IV) oxide Dry ice (solid phase) Identifiers CAS Number 124-38-9   Y 3D model (JSmol) Interactive image Interactive image 3DMet B01131 Beilstein Reference 1900390 ChEBI CHEBI:16526   Y ChEMBL ChEMBL1231871   N ChemSpider 274   Y ECHA InfoCard 100.004.271 EC Number 204-696-9 E number E290 (preservatives) Gmelin Reference 989 KEGG D00004   Y MeSH Carbon+dioxide PubChem CID 280 RTECS number FF6400000 UNII 142M471B3J   Y UN number 1013 (gas), 1845 (solid) InChI InChI=1S/CO2/c2-1-3   Y Key: CURLTUGMZLYLDI-UHFFFAOYSA-N   Y InChI=1/CO2/c2-1-3 Key: CURLTUGMZLYLDI-UHFFFAOYAO SMILES O=C=O C(=O)=O Properties Chemical formula C O 2 Molar mass 44.01 g·mol −1 Appearance Colorless gas Odor Low concentrations: none High concentrations: sharp; acidic [1] Density 1562 kg/m 3 (solid at 1 atm and −78.5 °C) 1101 kg/m 3 (liquid at
            閱讀完整內容