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a^x = b^y = c^z = k: write each base as a power of k and use the given relation

This type of question, asked 2 times: CDS 2 2018, CDS 2 2019. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    15
    If ax=by=cza^x = b^y = c^z and abc = 1, then the value of 1x+1y+1z\frac{1}{x} + \frac{1}{y} + \frac{1}{z} will be equal to

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  2. Question 2

    CDS 2 2019

    47
    If ax=by=cza^x = b^y = c^z and b2=acb^2 = ac, then what is 1x+1z\frac{1}{x} + \frac{1}{z} equal to ?

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  3. Question 3

    CDS 2 2019

    37
    If 3x=4y=12z3^x = 4^y = 12^z, then z is equal to

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