Question

Hello Mate!

Hope you all are having a good day.

A question for You all

${2}^{x} = {3}^{y} = {12}^{z} \\ show \: that \: \frac{1}{z} = \frac{1}{y} + \frac{1}{x}$
Hope I will get the best answer.

Answer 1

Let 2^x = 3^y = 12^z= k
So,
2 = k^(1/x)
3= k^(1/y)
12= k^(1/z)

We know that
2*2*3 =12
k^(1/x)*k^(1/x)*k^(1/y) = k^(1/z)
k^(1/x+1/x+1/y) = k^(1/z)

We know if base is same on both sides,then powers must be equal.

2/x + 1/y = 1/z
So this is the correct relation, I think the one asked in the ques is wrong.

Answer 2

Answer:

HEY DUDE!!

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