Decide given complexity of given function
This answer assumes that $\log$ is to the base 2.

Consider $n = 2^{1000}$. Then
$$
f(n) = 2^{1000}, \quad g(n) = (\log_2 2^{1000})^{100} = (1000)^{100} &lt; (1024)^{100} = (2^{10})^{100} = 2^{1000}.
$$
If you increase $n$ even more, you will see an even more dramatic difference between $f(n)$ and $g(n)$. You just have to consider large enough $n$, perhaps too large for your calculator.

What this example shows that even though $f(n)$ grows faster than $g(n)$, for values of $n$ encountered in practice the situation is very different, with $g(n)$ being much larger than $f(n)$. This shows the limits of asymptotic analysis – it is a natural and useful mathematical notion, but it isn't always a good model for reality.