Question

If 2^x =3^y=6^z ,prove that 1/x+1/y+1/z=0 or z=xy/x+y

Answer 1

Let 2^x = 3^y = 6^z = k
This means that,

x = log k base 2
y = log k base 3
And,
z = log k base 6

Now,
1/x = 1/log k base 2 = log 2 base k
Similarly,
1/y = log 3 base k

And
1/z = log 6 base k

Now,
1/x + 1/y = log 2 base k + log 3 base k = log 6 base k = 1/z

Hence proved that,

1/x + 1/y = 1/z

Hope this helps you !

Answer 2

hlo

hope the attachment will help u