If $a^{x} = b, b^{y} = c a n d c^{z} = a$ then $x y z = 1$

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Solution

Given: $a^{x} = b, b^{y} = c a n d c^{z} = a$

$a^{x} = b$

Raising both sides to the power $y z$ we get

$a^{x y z} = b^{y z}$

= $(b^{y})^{z}$

= $c^{z}$

= $a$

Since` $a^{x y z} = a$ , we get $x y z = 1$

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