
Example: Find the value of log_{3Ö3}81. Solution: let log_{3Ö3}81 = x By the definition of logarithm (3Ö3)^{x} = 81 But 3 = Ö3 * Ö3 = (Ö3)^{2} 81 = 3 * 3 * 3 * 3 = 3^{4} = [(Ö3)^{2}]^{4} = (Ö3)^{8} (Ö3 . Ö3 . Ö3)^{x} = (Ö3)^{8} ((Ö3)^{3})^{x} = (Ö3)^{8} Bases are equal and so indicies are equal. 3x = 8 Therefore, x = 3/8 i.e.,log_{3Ö3}81 = 8/3. Directions: Solve the following problems. Also write at least ten examples of your own. 