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If x = y^z , y = z^x and z = x^y , then

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asked Nov 11, 2020 in Exponents by Eihaa (49.3k points)
closed Nov 13, 2020 by Eihaa

If x = y^z , y = z^x and z = x^y , then

(a) \(\frac{xy}{z} = 1\)

(b) xyz = 1

(c) x + y + z = 1

(d) xz = y

exponents
class-8

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1 Answer

+1 vote

answered Nov 11, 2020 by Naaz (46.3k points)
selected Nov 13, 2020 by Eihaa

Best answer

(b) xyz = 1

z = x^y = (y^z)^y (∵ x = y^z )

= y^zy = (z^x)^zy = z^xyz (∵ y = z^x)

∴ z¹ = z^xyz ⇒ xyz = 1

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