Difference between revisions of "2000 AIME I Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | The system of equations | ||
| + | <center><math>\begin{eqnarray*}\log_{10}(2000xy) - (\log_{10}x)(\log_{10}y) & = & 4 \\ | ||
| + | \log_{10}(2yz) - (\log_{10}y)(\log_{10}z) & = & 1 \\ | ||
| + | \log_{10}(2000zx) - (\log_{10}z)(\log_{10}x) & = & 0 \\ | ||
| + | \end{eqnarray*}</math></center> | ||
| + | |||
| + | has two solutions <math>(x_{1},y_{1},z_{1})</math> and <math>(x_{2},y_{2},z_{2})</math>. Find <math>y_{1} + y_{2}</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2000|n=I|num-b=8|num-a=10}} | |
Revision as of 18:32, 11 November 2007
Problem
The system of equations
\log_{10}(2yz) - (\log_{10}y)(\log_{10}z) & = & 1 \\ \log_{10}(2000zx) - (\log_{10}z)(\log_{10}x) & = & 0 \\
\end{eqnarray*}$ (Error compiling LaTeX. Unknown error_msg)has two solutions 
and 
. Find 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2000 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
