2019 AMC 12A Problems/Problem 12
Contents
[hide]Problem
Positive real numbers and satisfy and . What is ?
Solution
Let , then and . Then we have .
We equate , and get . The solutions to this are .
To solve the given,
-WannabeCharmander
Solution 2
Thus or
We know that .
Thus
Thus
Thus
Thus
Solving for , we obtain .
Easy resubstitution makes
Solving for we obtain .
Looking back at the original problem, we have What is ?
Deconstructing this expression using log rules, we get .
Plugging in our know values, we get or .
Our answer is 20
Solution 3
Multiplying the first equation by we obtain .
From the second equation we have .
Then, .
See Also
2019 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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All AMC 12 Problems and Solutions |
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