MathDB
System of Equations: Logs

Source:

January 5, 2007
logarithmsAMCAIMEalgebrasystem of equationsAIME Ibinomial theorem

Problem Statement

The system of equations \begin{eqnarray*}\log_{10}(2000xy) - (\log_{10}x)(\log_{10}y) & = & 4 \\ \log_{10}(2yz) - (\log_{10}y)(\log_{10}z) & = & 1 \\ \log_{10}(zx) - (\log_{10}z)(\log_{10}x) & = & 0 \\ \end{eqnarray*} has two solutions (x1,y1,z1) (x_{1},y_{1},z_{1}) and (x2,y2,z2). (x_{2},y_{2},z_{2}). Find y1+y2. y_{1} + y_{2}.
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