For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in (g(n)), or f(n) = (g(n)). For each pair, determine which relationship is correct. Justify your answer, using the method of limits discussed above.

a) f(n) = log n²; g(n) = log n + 5.

b) f(n) = n; g(n) = log n².

c) f(n) = log² n; g(n) = log n.

d) f(n) = log n²; g(n) = (log n)².

e) f(n) = 10; g(n) = log 10.

f) f(n) = 2ⁿ; g(n) = 3ⁿ.

g) f(n) = 2ⁿ; g(n) = nⁿ