Question

If 3( power x ) = 5 ( power y) = 75 (power z ) . show that z = xy / (2x + y)
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Answer 1

Answer:

$Let \: 3^{x} = 5^{y} = 75^{z} = k$

$3^{x} = k \implies 3 = k^{\frac{1}{x}} \: --(1)$

$5^{y} = k \implies 5 = k^{\frac{1}{y}} \: --(2)$

$75^{x} = k \implies 75 = k^{\frac{1}{z}} \: --(3)$

$75 = k^{\frac{1}{z}}$

$\implies 3 \times 5^{2} = k^{\frac{1}{z}}$

$\implies k^{\frac{1}{x}} \times \left(k^{\frac{1}{y}}\right)^{2} = k^{\frac{1}{z}}$

$\implies k^{\frac{1}{x}} \times k^{\frac{2}{y}} = k^{\frac{1}{z}}$

$\implies k^{\frac{1}{x} + \frac{2}{y}} = k^{\frac{1}{z}}$

$\implies \frac{1}{x} + \frac{2}{y} = \frac{1}{z}$

$\implies \frac{y+2x}{xy} = \frac{1}{z}$

$\implies \frac{xy}{y+2x} = z$

$Hence\: proved$

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Answer 2

Step-by-step explanation:

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