2002 AIME I Problems/Problem 6
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Problem
The solutions to the system of equations
![$\log_{225}x+\log_{64}y=4$](http://latex.artofproblemsolving.com/5/9/e/59e46a564aaaca905d62986e77523e98fa0618a5.png)
![$\log_{x}225-\log_{y}64=1$](http://latex.artofproblemsolving.com/1/2/2/1226b24f95e00e2b64504c177aa2b07818ebbd75.png)
are and
. Find
.
Solution
Let and let
.
From the first equation: .
Plugging this into the second equation yields and thus,
.
So,
.
And
.
Thus, .
See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |