Question

solve this problem ​

Answer 1

Question : If 2^x = 3^y = 12^z , show that 1/z = 1/y + 2/x

Answer :

Let 2^x = 3^y = 12^z = k

Thus,

We can say that :

2 = k^1/x ,

3 = k^1/y ,

12 = k^1/z

Now,

We know that,

12 = 2^2 × 3

Thus,

We can say that :

k^1/z = k^2/x × k^1/y

k^1/z = (k^2/x + 1/y)

Finally,

Comparing both sides ,

It's proved that :

1/z = 2/x + 1/y

Hence, Proved.

1/z = 1/y + 2/x