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