The board of law examiners has charge of the investigation and examination of all persons who initially apply for admission to the bar of this state. The board may adopt suitable regulations, subject to approval by the supreme court, concerning the performance of its functions and duties. Regulations adopted pursuant to this section need not be published pursuant to Act No. 88 of the Public Acts of 1943, being sections 24.71 to 24.82, inclusive, of the Compiled Laws of 1948, as amended. The board has the power of subpoena, and the authority to administer oaths, and to take testimony under oath, which may be exercised by any member of the board in cases of applicants for admission to the bar.