MathDB

System of logs.

Source:

November 28, 2005

logarithmsquadraticsalgebrasystem of equations

Problem Statement

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)

and

(x_2, y_2).

Find

\log_{30}{(x_1y_1x_2y_2)}.