Time-constructible functions definition
$|x|$ here means the length of the string $x$ over an alphabet $\Sigma$. Note that $x$ does not need to be a natural number.

So, $|2^{100}|$ is $100$ (but do remember that you MUST understand that you are encoding the natural number $2^{100}$ into string over finite alphabet) if we want to encode a natural number in binary. Therefore, $T(|2^{100}|) = T(100) = \log_2100$.

It would be type-safer to write $|\lfloor{2^{100}}\rfloor|$