  We consider three-flavor chiral perturbation theory ($\chi$PT) at zero
temperature and nonzero isospin ($\mu_{I}$) and strange ($\mu_{S}$) chemical
potentials. The effective potential is calculated to next-to-leading order
(NLO) in the $\pi^{\pm}$-condensed phase, the $K^{\pm}$-condensed phase, and
the $K^0/\bar{K}^0$-condensed phase. It is shown that the transitions from the
vacuum phase to these phases are second order and take place when,
$|\mu_I|=m_{\pi}$, $|{1\over2}\mu_I+\mu_S|=m_K$, and
$|-{1\over2}\mu_I+\mu_S|=m_K$, respectively at tree level and remains unchanged
at NLO. The transition between the two condensed phases is first order. The
effective potential in the pion-condensed phase is independent of $\mu_S$ and
in the kaon-condensed phases, it only depends on the combinations
$\pm{1\over2}\mu_I+\mu_S$ and not separately on $\mu_I$ and $\mu_S$. We
calculate the pressure, isospin density and the equation of state in the
pion-condensed phase and compare our results with recent $(2+1)$-flavor lattice
QCD data. We find that the three-flavor $\chi$PT results are in good agreement
with lattice QCD for $\mu_I<200$ MeV, however for larger values $\chi$PT
produces values for observables that are consistently above lattice results.
For $\mu_I>200$ MeV, the two-flavor results are in better agreement with
lattice data. Finally, we consider the observables in the limit of very heavy
$s$-quarks, where they reduce to their two-flavor counterparts with
renormalized couplings. The disagreement between the predictions of two and
three flavor $\chi$PT can largely be explained by the differences in the
experimental values of the low-energy constants.
