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Question Number 161096 by HongKing last updated on 11/Dec/21

$$\mathrm{if}\mathrm{x};\mathrm{y};\mathrm{z}>0\mathrm{and}\mathrm{a};\mathrm{b};\mathrm{c}>0$$$$\mathrm{different}\mathrm{in}\mathrm{pairs}\mathrm{and}\mathrm{n};\mathrm{k}\in {\mathbb{N}}^{\ast }$$$$\frac{\log {\mathrm{x}}^{\mathbf{n}}}{{\mathrm{b}}^{\mathbf{k}}-{\mathrm{c}}^{\mathbf{k}}}=\frac{\log {\mathrm{y}}^{\mathbf{n}}}{{\mathrm{c}}^{\mathbf{k}}-{\mathrm{a}}^{\mathbf{k}}}=\frac{\log {\mathrm{z}}^{\mathbf{n}}}{{\mathrm{a}}^{\mathbf{k}}-{\mathrm{b}}^{\mathbf{k}}}$$$$\mathrm{then}\mathrm{find}\sqrt{\mathbf{xyz}}$$

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