How can I solve a system of 3 equations that use logs?

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I'm having a bit of trouble solving this system of equations. What would be a good way of solving for the three variables in a question like this? I've tried many different ways of substituting or eliminating parts of this system but I can't seem to get on the right path with this one.

(logx)(logy) - 3log5y - log8x = -4
(logy)(logz) - 4log5y - log 16z = 4
(logz)(logx) - 4log8x -3log625z = -18