prove that if $\displaystyle a^{x} = b^{y} = (ab)^{xy} $ than $\displaystyle x+y =1 $

A not really sure how to start,

what I have done so far;

$\displaystyle a^{x} = b^{y} $

$\displaystyle xlog_{a} a = ylog_{a} b $

$\displaystyle x =ylog_{a} b $

is this correct

where do I go from here?

$\displaystyle ab^{xy} $

$\displaystyle xylog_{a} (ab) $

$\displaystyle xlog_{a} a + ylog_{a} b $

is this also correct ?