If $a^{x} = b^{y} = c^{z}$ and $a, b, c$ are in G.P ., then $x, y, z$ are in

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Solution

Finding the value:
Given $a, b, c$ are in G.P and $a^{x} = b^{y} = c^{z}$
$L e t a^{x} = b^{y} = c^{z} = p a = p^{1 / x} b = p^{1 / y} c = p^{1 / z} b^{2} = a c (\sin c e a, b, c i n G P) {(p^{1 / y})}^{2} = p^{1 / x} p^{1 / z} p^{2 / y} = p (1 / x + 1 / y) E q u a t i n g p o w e r s o f p 2 / y = 1 / x + 1 / z S o x, y, z a r e i n H P .$
The terms $x, y, z$ are in H.P

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