Question

If p = a^x, q = a^y and a^4 = (p^4y.q^4x)^x prove that xyz =1/2​

Answer 1

It is given that P = a^x , q = a^y and a⁴ = (p^4y q^4x)^z

we have to prove that xyz = 1/2.

here a^4 = (p^4y . q^4x)^z

⇒a^4 = [(a^x)^(4y) . (a^y)^4x ]^z

⇒a^4 = [a^(4xy) . a^(4xy)]^z

⇒a^4 = [a^(4xy + 4xy)]^z

⇒a^4 = [a^(8xy)]^z

⇒a^4 = a^(8xyz)

⇒4 = 8xyz

⇒xyz = 1/2

hence proved

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