In p q r \neq 0 and p^{-x}=\frac{1}{q}, q^{y}=\frac{1}{r}, r^{z}=\frac{1}{p}, what is the value of the product xyz?

GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 6 of 65

Marks: +1, -0

p q r ≠ 0

and

p^{-x}=\;{1}/{q}, q^{y}=\;{1}/{r}, r^{z}=\;{1}/{p}

, what is the value of the product xyz?

Solution:

p^{x}=q

q^{y}=r

x \log p=\log q

y \log q=\log r

z \log r=\log p

x=\;{\log q}/{y p}

y=\;{y z}/{\log q}

z=\;{\log p}/{y r}

x × y × z=1

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