The council shall provide for the method by which its building or setback regulations shall be enforced and shall provide for a board of adjustment with powers to modify or vary the regulations, in specific cases, in order that unwarranted hardships, which constitute an unreasonable deprivation or use as distinguished from the mere grant of a privilege, may be avoided, the intended purpose of the regulations being strictly observed and the public welfare and public safety protected. If there is a board of zoning adjustment such board shall be appointed to serve as the board of adjustment for the building or setback line regulations. Regulations authorized under the provisions of this section shall not be adopted, changed or amended until a public hearing has been held thereon by the commission, public notice of which shall be given in the manner provided by law. Appeals may be taken from any order, regulation or action of a board of adjustment as provided in this section in the manner provided by law for appeals from orders of the board of adjustment in zoning cases.