If logxx(y+z−x)=logyy(z+x−y)logzz(x+y−z),provethatxyyx=zxyz=xzzx

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Question

If $\frac{x ( y + z - x )}{lo g x} = \frac{y ( z + x - y )}{lo g y} \frac{z ( x + y - z )}{lo g z}, p r o v e t h a t x^{y} y^{x} = z^{x} y^{z} = x^{z} z^{x}$

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\frac{x ( y + z - x )}{lo g x} = \frac{y ( z + x - y )}{lo g y} \frac{z ( x + y - z )}{lo g z}, p r o v e t h a t x^{y} y^{x} = z^{x} y^{z} = x^{z} z^{x}

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Question Text

\frac{x ( y + z - x )}{lo g x} = \frac{y ( z + x - y )}{lo g y} \frac{z ( x + y - z )}{lo g z}, p r o v e t h a t x^{y} y^{x} = z^{x} y^{z} = x^{z} z^{x}