Looking at time complexity explanations and found some general rules for determining big-O notation, which made sense, but then found some problems listed as being for the same stuff that are like:
In each of the following situations indicate whether $f = O(g)$ or $f = Ω(g)$, or both (in which case $f = Θ(g)$), and present your proof clearly.
$f(n) = 10\log(n)$
$g(n) = \log(n^2)$
Can some one explain how I'm supposed to go about solving/proving this? I know things about big-O like only using the highest exponent polynomial term in it, but not of what else I seen really does any good here.
You need the law of logarithms $\log (a^b)=b\log(a)$