6

Part of 2002 AIME Problems

Problems(2)

System of logs.

Source:

The solutions to the system of equations \begin{eqnarray*} \log_{225}{x}+\log_{64}{y} &=& 4\\ \log_x{225}-\log_y{64} &=& 1 \end{eqnarray*} are

(x_1,y_1)

(x_2, y_2).

\log_{30}{(x_1y_1x_2y_2)}.

logarithmsquadraticsalgebrasystem of equations

Another Frac. Decomposition Problem

Source:

Find the integer that is closest to

1000 \sum_{n=3}^{10000}\frac{1}{n^{2}-4}.