Question

2^x=3^y=6^-z prove that 1/x+1/y+1/z=0

Answer 1

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

let 2^x=3^y=6^-z=k

so

2=k^1/x, 3=k^1/y, 6=k^-1/z

since 2×3=6

k^1/x× k^1/y=k^-1/z

k^1/x+1/y=k^-1/z

1/x+1/y=-1/z

hence

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