The purpose of this article is proving the equality of two natural L-invariants attached to the adjoint representation of a weight one cusp form, each defined by purely analytic, respectively, algebraic means. The proof departs from Greenberg's definition of the algebraic L-invariant as a universal norm of a canonical Zp-extension of Qp associated to the representation. We relate it to a certain 2 × 2 regulator of p-adic logarithms of global units by means of class field theory, which we then show to be equal to the analytic L-invariant computed in Rivero and Rotger [J.