14. 计算:
$$
\left(\sum_{k=1}^{20} \log _{5^{k}} 3^{k^{2}}\right)\left(\sum_{k=1}^{100} \log _{9} 25^{k}\right)=(\quad) \text {. }
$$
(A) 21
(B) $100 \log _{5} 3$
(C) $200 \log _{3} 5$
(D) 2200
(E) 21000
14. E.
$$
\begin{array}{l}
\left(\sum_{k=1}^{20} \log _{5} k^{k^{2}}\right)\left(\sum_{k=1}^{100} \log _{9} 25^{k}\right) \\
=\left(\sum_{k=1}^{20} \frac{k^{2}}{k} \log _{5} 3\right)\left(\sum_{k=1}^{100} \log _{9} 25\right) \\
=\log _{5} 3\left(\sum_{k=1}^{20} k\right) \cdot 100 \log _{3} 5 \\
=100 \sum_{k=1}^{20} k=21000 .
\end{array}
$$