If $a^{x} = c^{q} = b$ and $c^{y} = a^{z} = d$ , then ___.

x y = q z

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\frac{x}{y} = \frac{q}{z}

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x + y = q + z

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x - y = q - z

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Solution

The correct option is D $x y = q z$
Taking $log$ on every side, we get
$x log a = q log c = log b \dots$ eqn (1)
$z log a = y log c = log d \dots$ eqn (2)
Divide eqn (1) with eqn (2)
$\Rightarrow \frac{x}{z} = \frac{q}{y}$

$\Rightarrow x y = q z$

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