The city council shall constitute the board of equalization for the city, and shall have power as such board to equalize all taxes and assessments, to correct any errors in the listing or valuation of property, and to supply any omissions in the same. A majority of all the members elected to the council shall constitute a quorum for the transaction of business properly before the board, but a less number may adjourn from time to time and compel the attendance of absent members. When sitting as a board of equalization on general or special taxes the council may adopt rules and regulations as to the manner of presenting complaints and applying for relief. It shall not invalidate or prejudice the proceedings of the board that a majority of the members thereof after organization as a board do not in fact continue present during the advertised hours for the sitting of such board; Provided, however, the clerk and some member of the board shall be present to receive complaints or applications for relief. No final action shall be taken with respect to any taxes or assessments by the board until a majority of the members of the council sitting as a board of equalization shall be present and in open session.