LogAndExp
AIME
2016
Let $x,y,$ and $z$ be real numbers satisfying the system $\log_2(xyz-3+\log_5 x)=5$ $\log_3(xyz-3+\log_5 y)=4$ $\log_4(xyz-3+\log_5 z)=4$ Find the value of $|\log_5 x|+|\log_5 y|+|\log_5 z|$.
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