L O G C E P T I O N
Source: 2016 AIME II #3
March 17, 2016
AMCAIMEAIME II
Problem Statement
Let and be real numbers satisfying the system \begin{align*}
\log_2(xyz-3+\log_5 x) &= 5 \\
\log_3(xyz-3+\log_5 y) &= 4 \\
\log_4(xyz-3+\log_5 z) &= 4.
\end{align*} Find the value of .