During my internet adventures browsing theological articles and blogs, I somehow picked up the idea that in a similar way to Catholics, Lutherans believe in baptismal regeneration and that baptism is, therefore, necessary for salvation.
I also picked up the idea that Lutherans have a robust "high" sacramental theology, similar to Catholics. However, perusing the Wikipedia article on "Lutheran Sacraments" reveals that Lutherans only believe in 3 sacraments, not 7.
I'm wondering, does Lutheranism believe that their sacraments are necessary for salvation (Baptism, Eucharist, Penance)? And if so, how do they reconcile that with the classic Protestant "Salvation by Faith alone" doctrine?