Complexity of an encoded turing machine

Question

This is an example of an assignment question, there are 3 of them so I created my own in order to better understand it.

First, we have the variable m which is a binary encoding such as 100#001#010 which is translated to [4, 1, 2]

Next is the variable n = the total length of the input/encoding

And k which is the largest number in the list (4 in the previous list)

Now we set $f(n)$ as the turing machine that took m as input, and want to see if $f(n) = O(g(n))$ where $g(n)$ is a polynomial.

How can I solve this on $f(n) = m (log (n)) (log (k))$?