# Logs have never been so much fun

Algebra Level pending

If $$\begin{cases} x =\log_c b +\log_{ b }{ c } \\ y=\log_{ a }{ c } +\log_{ c }{ a } \\ z = \log_{ b }{ a } +\log_{ a }b\end{cases}$$,

then find the value of $$x^2 + y^2 + z^2 - xyz$$.

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