MATHEMATICAL PRIMER FOR CS4102 1. Logarithms and ...
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MATHEMATICAL PRIMER FOR CS4102. 1. Logarithms and Exponentials. The
logarithm of x with respect to base b is the value y such that by = x. In this sense,.
MATHEMATICAL PRIMER FOR CS4102
1. Logarithms and Exponentials The logarithm of x with respect to base b is the value y such that by = x. In this sense, taking logarithms is the inverse of raising to a power. We will almost always use logarithms that are base 2. Thus, when you see log(x), it typically means log2 (x). This Wikipedia article here has more details. (1) (2) (3) (4) (5) (6) (7) (8) (9)
blogb x = x and logb (bx ) = x logb ( xy ) = logb (x) − logb (y) logb (xy) = logb (x) + logb (y) logk (n) = (logn)k log log n = log(log n) a0 = 1, a1 = a (am )n = amn = (an )m am an = am+n a−1 = a1 2. Series
Here are some basic series identities; see Appendix A of CLRS for more details. (1) Simple arithmetic series: n X 1 k = 1 + 2 + · · · + n = n (n + 1) 2 k=1
