Q. If 2^x=3^y=6^z, Prove that: 1/x+1/y=1/z.

Solution:

Here, 2^x=3^y=6^z

i.e. 2^x=6^z

or, 2=6^(z/x)

Also, 3^y=6^z

or, 3=6^(z/y)

We know, 2*3=6

or, 6^(z/x)*6^(z/y)=6

or, (z/x)+(z/y)=1

or z(1/x+1/y)=1

Therefore, 1/x+1/y=1/z