Log rules are interesting

$\log_{7x}m=6$

$\frac{ \log{m}}{\log{7x}} =6$

$\frac{ \log{7x}}{\log{m}} =\frac{1}{6}$

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$\log_{8y}m=10$

$\frac{ \log{m}}{\log{8y}} =10$

$\frac{ \log{8y}}{\log{m}} =\frac{1}{10}$

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$\log_{9z}m=15$

$\frac{ \log{m}}{\log{9z}} =15$

$\frac{ \log{9z}}{\log{m}} =\frac{1}{15}$

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$log_{504xyz}m^{2016}=n$

$2016 \times \frac{ \log{m}}{\log{7x \times 8y \times 9z}}=n$

$\frac{1}{2016} \times \frac{ \log{7x \times 8y \times 9z}}{\log{m}}= \frac{1}{n}$

$\frac{1}{2016} \times ( \frac{\log{7x}}{\log{m}}+\frac{ \log{8y}}{\log{m}}+\frac{ \log{9z}}{\log{m}})= \frac{1}{n}$

$\frac{1}{2016} \times ( \frac{1}{6}+\frac{1}{10}+\frac{1}{15})= \frac{1}{n}$

$\frac{1}{2016} \times \frac{1}{3}= \frac{1}{n}$

$\frac{1}{6048}= \frac{1}{n}$

$n=6048$