Let x, y, z and W be positive numbers such that log_x W=24, log_y W=40 and log_xyzW=12, then log_zW=

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Detailed Solution

$w = x^{24} \Rightarrow x = w^{\frac{1}{24}}$

$w = y^{40} \Rightarrow y = w^{\frac{1}{40}}$

$w = (xyz)^{12} \Rightarrow z = w^{\frac{1}{12} - \frac{1}{24} - \frac{1}{40}} = w^{\frac{1}{60}} \Rightarrow \log_{z} w = \log_{w^{\frac{1}{60}}} w = 60$

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