1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Big Oh and Logs

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data

    What is the order of the two functions:

    f(n) = (log(n^3))^4
    g(n) = (log(n^7))^2

    2. Relevant equations


    3. The attempt at a solution

    f(n) = (log(n^3))^4 = log(n^3) * log(n^3) * log(n^3) * log(n^3)

    g(n) = (log(n^7))^2 = log(n^7) * log(n^7)

    Based on the Big Oh rules (the link above) using Log of a Power Rule we see that for one log(n^3) and one log(n^7) the order is O(log n) and O(log n). Now since f(n) is raised to power of 4 the order is now O(log n)^4 and g(n) is raised to power of 2 so O(log n)^2.

    Now using Comparison Rule 2 we that f(n) is O(n^4) and g(n) is O(n^2).

    Would this reasoning be correct?
    Last edited: Sep 21, 2008
  2. jcsd
  3. Sep 22, 2008 #2
    I'm not sure how you used comparison rule 2 to get that. Everything up until there is fine though.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook