2016 AIME II Problems/Problem 3
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