Formulas for logarithms. Formulas and examples: log_a 1 = 0, log_3 1 = 0, log_(1/2) 1 = 0, log_a a = 1, log_3 3 = 1, log_(1/2) (1/2} = 1, log_a a^k = k, log_2 2^3 = 3, log_5 5^3 = 3, log_a x^k = k * log_a x, log_3 2^5 = 5 * log_3 2, log 3^4 = 4 * log 3, a^(log_a x) = x, 3^(log_3 5) = 5, (1\o2)^(log_(1/2) 7) = 7, log_a (x\c y) = log_a x + log_a y, log_2 3/5 = log_2 3 + log_2 5, log_3 (9 * square root of 3) = log_3 9 + log_3 square root of 3, log_a x/y = log_a x - log_a y log_2 3/5 = log_2 3 - log_2 5, log_3 (square root of 3 / 9) = log_3 squre root of 3 - log_3 9, log_a b = log_c b / log_c a, c - any number which fulfill the conditions , log_2 3 = log_11 3 / log_11 2, log_2 3 = log_15 3 / log_15 2, log_a b = 1 / log_b a, log_3 8 = 1 / log_8 3.