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If 2^x = 3^y =12^z show that 1/z= 1/y...

If `2^x = 3^y =12^z` show that `1/z= 1/y+2/x` ​ ​

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Let `2^x=3^y=12^ z=k`
Then, `2=k ^(1/x),3=k ^(1/y)` and `12=k ^(1/z)`
Now,` 12=k ^(1/z)` so,`(2^2)xx3=k ^(1/z)` so,`(k^(1/x)) ^ 2×k ^(1/y)=k^(1/z)` [since `2=k ^(1/x)` and `3=k^(1/y)`]
so, `k^(2/x)+k^(1/y)=k^(1/z)`
so, ...
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