Always approach Logarithms with uncertainty. a bit confused by Log of power rule. Hope to receive some simple clarifications. Found this post very interesting. Where we basically have $T(n) = \Theta(n^{\log_2 3})$. as we plug in $2^n$, shouldn't it become \begin{equation} \Theta(2^{n^{\log_2 3}}) \end{equation}.
If so, we can't do any further simplification, can we ?
or it is correct to have
$T(2^n) = \Theta(2^{n\log_2 3})$.
if so, what if we plug in $2^{n^{n}}$, what should it be ?
$T(2^n)$ is not $2^{n^{\log_23}}$, it's $(2^n)^{\log_23}=2^{n\log_23}$.