Yes, they are. Bronsted-Lowry acids are proton donors that can be thought of as electron pair acceptors because the H⁺ is transferred to the electron pair on a base. Bronsted-Lowry bases are proton acceptors. In order to accept a proton, the base must donate an electron pair to the proton, so Bronsted-Lowry bases are also Lewis bases. It is important to note that the converse is not true--all Lewis acids and bases are not Bronsted-Lowry acids and bases.

Note the use of the equilibrium constant to solve the problem and the assumption that the amount of dissociation for weak acids is quite small. That assumption is only valid for a weak acid in a solution where the weak acid concentration is much larger than the value of x. If x is greater than 5% of the initial concentration of the acid, then you must solve the quadratic equation because the assumption becomes invalid.

Note the important relationships between K _w, K _a, and K _b necessary for solving this problem.