If \( \frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b} \), show that \( a^{a} \cdot b^{b...

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If \( \frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b} \), show that \( a^{a} \cdot b^{b} \cdot c^{c}=1 \)
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