Answer
$2; 2;$
Work Step by Step
We are given:
$$\begin{cases}
1\text{ googol}&=10^{100}\\
1\text{ googolplex}&=10^{googol}.
\end{cases}$$
Calculate $\log(\log{(\text{googol})})$:
$$\begin{align*}
\log(\log{(\text{googol})})&=\log(\log 10^{100})\\
&=\log 100\\
&=\log 10^2\\
&=2.
\end{align*}$$
Calculate $\log\log(\log{(\text{googolplex})}))$:
$$\begin{align*}
\log(\log(\log{(\text{googolplex})}))&=\log(\log(\log 10^{\text{googol}}))\\
&=\log (\log (\text{googol}))\\
&=2.
\end{align*}$$
