2016 AIME II Problems/Problem 3
Let and be real numbers satisfying the system , , , Find the value of .
Solution
First, we get rid of logs by taking powers: , , and . Adding all the equations up and using the property, we have , so we have . Solving for by substituting for in each equation, we get , so adding all the absolute values we have .
Solution by Shaddoll
See also
2016 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |