# Logarithm System

Algebra Level 2

$\Large\begin{cases} \log_x w & = & 24 \\ \log_y w & = & 40 \\ \log_{xyz} w & = & 12 \end{cases}$

If $$x,y,z$$ are real numbers greater than 1 and $$w$$ is a positive number satisfying the system above, then find the value of $$\left (\log_w z \right)^{-1}$$.

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