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?