Question

Solve
$if \: 2^{x} = 3^{2} = 6 ^{?} .\\ then \: prove \: z = \frac{xy}{x + y}$
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Answer 1

Given : 2^x = 3^y = 6^z

To Prove : z = xy/(x+y)

Let, 6^z = k. => 6 = k^1/z

Therefore, 2^x = k => 2 = k^1/x

3^y = k => 3 = k^1/y

Now, 6 = 2×3

=> k^1/z = k^1/x × k^1/y

=> k^1/z = k^(1/x + 1/y)

=> 1/z = 1/x + 1/y

=> z = xy/(x+y) [proved]