I have been trying to understand big O notation for log functions. Consider the following two functions: $$f(x) = log_2x $$ $$g(x) = log_3x $$
Now, with a little bit of research that I did, I realized that
because the same logs with different bases differ from each other by a constant and hence the above two points make sense.
Now I am trying to understand the behavior of the following two functions: $$f(x)= n^5$$ $$g(x)= 5^n$$
Can someone help me reason as to how do I go about understanding the big O notation for these two functions like I did for the log function