The value of $\dfrac{1}{log_{xy}xyz}+\dfrac{1}{log_{yz}xyz}+\dfrac{1}{log_{zx}xyz}$ is
$\dfrac{1}{log_{xy}xyz}+\dfrac{1}{log_{yz}xyz}+\dfrac{1}{log_{zx}xyz}$
= $log_{xyz} xy + log_{xyz} yz + log_{xyz} zx$
=$log_{xyz}(xy \times yz \times zx)$
=$log_{xyz}(xyz)^{2}$
= $2log_{xyz}xyz$
= 2 x 1
= 2
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