If $p^{x} = r^{y} = m$ and $r^{w} = p^{z} = n$ , then which one of the following is correct?

x w = y z

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x z = y w

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x + y = w + z

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x - y = w - z

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Solution

The correct option is A $x w = y z$
$p^{x} = r^{y} \Rightarrow p = r^{y / x}$ .....(i)
Also $p^{z} = r^{w} \Rightarrow p = r^{w / z}$ .....(ii)
From (i) and (ii), we have
$p = r^{y / x} = r^{w / z} \Rightarrow \frac{y}{x} = \frac{w}{z}$
Therefore, $y z = x w$

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