Question

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Answer 1

Step-by-step explanation:

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Answer 2

Given :-

$2 {}^{x} = 3 {}^{y} = 6 {}^{z}$

What to prove :-

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

Solution :-

$let \: 2 {}^{x} = 3 {}^{y} = 6 {}^{z} = k$

Hence,

$→ \: \: 2 {}^{x} \: = k \\ \: \: \: \: \: \: \: \: \: \: \: 2 = k {}^{ \frac{1}{x} } \\ \\→ 3 {}^{y } = k \\ \: \: \: \: \: \: 3 = k {}^{ \frac{1}{y} } \\ \\→ 6 {}^{z} = k \\ \: \: \: \: \: \: \: \: 6 = k {}^{ \frac{1}{z} } \\ \\ ∵ \: 6 = 3\times 2\\ \\ ∴k {}^{ \frac{1}{z} } = k {}^{ \frac{1}{y} } \times k {}^{ \frac{1}{x} } \\ \\ k {}^{ \frac{1}{z} } = k {}^{( \frac{1}{y} + \frac{1}{x} )} \\ \\ ∴ \frac{1}{z} = \frac{1}{y} + \frac{1}{x} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: proved$