If \( \frac{\log a}{y-z}=\frac{\log b}{z-x}=\frac{\log c}{x-y} ; \) prove that \( a^{y+z} \cdot ...

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If \( \frac{\log a}{y-z}=\frac{\log b}{z-x}=\frac{\log c}{x-y} ; \) prove that \( a^{y+z} \cdot b^{z+x} \cdot c^{x+y}=1 \)
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