Two choices , if you do not want to write answer , you can directly check my answer. if you want to write your answer, that is ok

For each pair of functions determine if f(n) (g(n)) or f(n) (g(n)) or f(n) O(g(n)) and provide a proof as specified.

give a proof using the definitions. f(n) = log3 (n), g(n) = log2 (n)

The answer:

f(n) = (g(n))

f(n) =log3 (n)=logn/log3

g(n) = (logn)^2 = logn * logn

Let me define a unknown symbol#,which can be = or < or > ..every symbols

f(n) # g(n)

logn/log3 # logn * logn

1/log3 # logn

1#log3*logn

2.096#logn

n#10^(2.096)

n#124.7

So when n > 124.7 , # is equal to >

f(n)>g(n)

f(n) c*g(n)

f(n) = (g(n))

when n< 124.7 , # is equal to <

f(n)

f(n) c*g(n)

f(n) = O(g(n))