
Example: Find the value of log_{Öa} Ö(a^{6/7}). Solution: Let log_{Öa} Ö(a^{6/7}) = x By definition of logarithm, (Öa)^{x} = Ö(a^{6/7}) = (a^{6/7})^{1/2} = a^{6/7 * 1/2} = a^{3/7} a = Öa * Öa = (Öa)^{2} (Öa)^{x} = (Öa)^{2})^{3/7} = (Öa)^{2*3/7} (Öa)^{x} = (Öa)^{6/7} Bases are equal so indices are equal. Therefore, x = 6/7 i.e., log_{Öa} Ö(a^{6/7}) = 6/7 Directions: Solve the following problems. Also write at least ten examples of your own. 