If $a^{x} = b, b^{y} = c, c^{z} = a,$ , then the value of $x y z$ is:

0

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1

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\frac{1}{a b c}

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a b c

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Solution

The correct option is D $1$
Given, $a^{x} = b, b^{y} = c$ and $c^{z} = a$
Taking $log$ on both sides, we get
$x log a = log b \Rightarrow x = \frac{log b}{log a}$
$y log b = log c \Rightarrow y = \frac{log c}{log b}$
$z log c = log a \Rightarrow z = \frac{log a}{log c}$
Now $x y z = \frac{log b}{log a} \times \frac{log c}{log b} \times \frac{log a}{log c} = 1$

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