2. Given two lines $l_{1}: y=2, l_{2}: y=4$, let the graph of the function $y=3^{x}$ intersect $l_{1} 、 l_{2}$ at points $A 、 B$, and the graph of the function $y=5^{x}$ intersect $l_{1} 、 l_{2}$ at points $C 、 D$. Then the coordinates of the intersection point of lines $A B$ and $C D$ are $\qquad$
2. $(0,0)$.
$$
\begin{array}{l}
\text { It is easy to see that } A\left(\log _{3} 2,2\right), B\left(\log _{3} 4,4\right), \\
C\left(\log _{5} 2,2\right), D\left(\log _{5} 4,4\right) . \\
\text { Then } k_{A B}=\frac{4-2}{\log _{3} 4-\log _{3} 2}=\frac{2-0}{\log _{3} 2-0}=k_{O A}, \\
k_{C D}=\frac{4-2}{\log _{5} 4-\log _{5} 2}=\frac{2-0}{\log _{5} 2-0}=k_{o c} .
\end{array}
$$

Therefore, $O, A, B$ and $O, C, D$ are collinear respectively. Hence, the lines $A B$ and $C D$ intersect at the origin $O(0,0)$.