# Logarithms?

Algebra Level 4

$\large \begin {cases} x^{xyz} =y^2 \\ y^{xyz+1}=z^3 \\ z^{xyz+2}=x^4 \end {cases}$

Let $$x$$, $$y$$ and $$z$$ be positive integers that satisfy the system of equations above. Find the sum of all possible $$x,y,z$$.

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