Properly Solving a Big-O Proof
I am currently taking a class which is incorporating a topic I have not yet had much experience with - Big-O. Here is an example of the type of questions I will need to answer. Please note: these questions resemble that of those which I will need to do for homework, however, the numbers, etc. are changed. 

I am **not** looking for *solutions*. I am looking for an explanation on how to effectively write the proof up.

The problems look like this (the first equation is f(n) the second is g(n)):

    (a) 5^(log_5(n)) and 3n+2
    (b) n^2 and sqrt(3)^(log(n))

I understand that, to effectively write the proof, I must prove that

    |f(x)| <= c|g(x)| for all x >= k
(k == n_0 depending on how you were taught)
So for the first one I simplify the question to

    n is O(3n+2)

and I'm not entirely certain how to begin the second one.

From here, how do I pick values c and k? Are they simply arbitrary values which just make the equation true or is there something more which I am missing? I have seen many examples, but none of these explain how they are getting their values for c and k.

Thanks for your help!
Properly Solving a Big-O Proof
===

I am currently taking a class which is incorporating a topic I have not yet had much experience with - Big-O. Here is an example of the type of questions I will need to answer. Please note: these questions resemble that of those which I will need to do for homework, however, the numbers, etc. are changed. 

I am **not** looking for *solutions*. I am looking for an explanation on how to effectively write the proof up.

The problems look like this (the first equation is f(n) the second is g(n)):

    (a) 5^(log_5(n)) and 3n+2
    (b) n^2 and sqrt(3)^(log(n))

I understand that, to effectively write the proof, I must prove that

    |f(x)| <= c|g(x)| for all x >= k
(k == n_0 depending on how you were taught)
So for the first one I simplify the question to

    n is O(3n+2)

and I'm not entirely certain how to begin the second one.

From here, how do I pick values c and k? Are they simply arbitrary values which just make the equation true or is there something more which I am missing? I have seen many examples, but none of these explain how they are getting their values for c and k.

Thanks for your help!