  We use the elliptic regulator to recover some identities between Mahler
measures involving certain families of genus 2 curves that were conjectured by
Boyd and proven by Bertin and Zudilin by differentiating the Mahler measures
and using hypergeometric identities. Since our proofs involve the regulator,
they yield light into the expected relation of each Mahler measure to special
values of $L$-functions of certain elliptic curves.
