Exponents & Logarithms Definition : ab c log a c b a : base a : base ; a 0, a 1 b : exponent b : logarithm ab : power c : argument ; c > 0 Properties of Exponent : Properties of Logarithms : 1. x m x n x m n 1. 10 y x y log x 2. x m x n x mn 2. log10x x 3. x y m xm ym 3. log a b log c b log c a m x xm 4. m y y 5. x m 6. x m n n 4. loga xy loga x loga y x mn x nm x n n xm 7. x m x n m m 1 xm x 5. log a log a x log a y y 6. log a x n n log a x 7. log x c logb x ; c is constant 8. log a b 8. x0 1 ; x 0 9. x1 x 1 log b a 9. log a b logb c log a c 10. log a b logb c logc d log a d Additional Properties : 1. n log am b n log a b m 2. a log a b b log 3. a am bn 11. log bn x 1 log b x n 12. log bn x n log b x 1 13. log 1 log b x x b b n m