Difference between revisions of "2016 AIME II Problems/Problem 3"
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Let <math>x,y,</math> and <math>z</math> be real numbers satisfying the system | Let <math>x,y,</math> and <math>z</math> be real numbers satisfying the system | ||
<math>\log_2(xyz-3+\log_5 x)=5</math> | <math>\log_2(xyz-3+\log_5 x)=5</math> |
Revision as of 19:09, 17 March 2016
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