If x=y^z, y= z^x and z=x^y, prove that: xyz = 1 | Indices | SciPiPupil

Question: If $x= y^z , y=z^x and z=x^y$, prove that: xyz = 1$

Solution:

Given,

$x= y^z , y=z^x and z=x^y$

To prove: $xyz = 1$

We know,

$x = y^z$

$or, x = (z^x)^z$

$or, x = z^{xz}$

$or, x = (x^y)^{xz}$

$or, x = x^{xyz}$

$or, x^1 = x^{xyz}$

$or, 1 = xyz$

$\therefore xyz = 1$

#proved

Related Notes and Solutions:

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