if-x-y-z-gt-0-and-a-b-c-gt-0-different-in-pairs-and-n-k-N-log-x-n-b-k-c-k-log-y-n-c-k-a-k-log-z-n-a-k-b-k-then-find-xyz-

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

if x;y;z>0 and a;b;c>0 different in pairs and n;k∈N^∗ ((log x^n )/(b^k - c^k )) = ((log y^n )/(c^k - a^k )) = ((log z^n )/(a^k - b^k )) then find (√(xyz))

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

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if-x-y-z-gt-0-and-a-b-c-gt-0-different-in-pairs-and-n-k-N-log-x-n-b-k-c-k-log-y-n-c-k-a-k-log-z-n-a-k-b-k-then-find-xyz-

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