2019 AMC 12A Problems/Problem 12
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
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 \boxed{B{}
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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