Question

2^x =4^y=8^z prove 1/z=1/x+1/y

Answer 1

2^x=2^2y=2^3z

2^x=2^2y or 2^2y=2^3z

x=2y or 2y=3z

x=3z

1/z=x+y/xy

1/z=(3z+3z/2)/3z(3z/2)

1/z=(6z+3z)/2/9z²/2

1/z=(9z)/9z²

1/z=1/z

Hence proved