Prove that x = 2yz/y – z.

If 2^x = 3^y = 12^z, prove that x = 2yz/y – z.

Solution:

It is given that

2^x = 3^y = 12^z

Consider

2^x = 3^y = 12^z = k

Here

2^x = k where 2 = (k)^1/x

3^y = k where 3 = (k)^1/y

12^z = k where 12 = (k)^-1/z

We know that

12 = 2 × 2 × 3

Therefore, it is proved.

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