(adsbygoogle = window.adsbygoogle || []).push({}); 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

http://www.augustana.ca/~hackw/csc210/exhibit/chap04/bigOhRules.html

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?

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# Homework Help: Big Oh and Logs

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