Question

if a^x=b^y=c^z and abc=1 then prove 1/x +1/y+1/z=0

Answer 1

Let a^x=b^y=c^z=k

Therefore,

a=k^(1/x)

b=k^(1/y)

c=k^(1/z)

As abc=1

k^(1/x).k^(1/y).k^(1/z)=1

k^(1/x+1/y+1/z)= 1 or k^0( as any number to the power 0 is 1)

Comparing the powers we get

1/x+1/y+1/z=0

Hence proved

Hope it was helpful:)