2. The integer solution $x$ of the equation $(\lg x)^{\lg (\lg x)}=10000$ is $x$ $=$ . $\qquad$
2. $10^{100}$.

Let $a=\lg x$. Then
$$
\begin{array}{l}
a^{\operatorname{Ig} a}=10^{4} \Rightarrow(\lg a)(\lg a)=\lg 10^{4}=4 \\
\Rightarrow \lg a= \pm 2 \Rightarrow \lg (\lg x)= \pm 2 .
\end{array}
$$

If $\lg (\lg x)=2$, then
$$
\lg x=10^{2} \Rightarrow x=10^{100} \text {; }
$$

If $\lg (\lg x)=-2$, then $\lg x=10^{-2} \Rightarrow x=10^{\frac{1}{100}}$ (discard).
Thus, the integer solution of the equation is $x=10^{100}$.