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1.442695 bits (log 2 e) – approximate size of a nat (a unit of information based on natural logarithms) 1.5849625 bits (log 2 3) – approximate size of a trit (a base-3 digit) 2 1: 2 bits – a crumb (a.k.a. dibit) enough to uniquely identify one base pair of DNA: 3 bits – a triad(e), (a.k.a. tribit) the size of an octal digit 2 2: nibble
Every family of sets with n different sets has at least log 2 n elements in its union, with equality when the family is a power set. [30] Every partial cube with n vertices has isometric dimension at least log 2 n, and has at most 1 / 2 n log 2 n edges, with equality when the partial cube is a hypercube graph. [31]
The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
For any number a in this list, one can compute log 10 a. For example, log 10 10000 = 4, and log 10 0.001 = −3. These are instances of the discrete logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
The log base 2 can be used to anticipate whether a multiplication will overflow, since ⌈log 2 (xy)⌉ ≤ ⌈log 2 (x)⌉ + ⌈log 2 (y)⌉. [53] Count leading zeros and count trailing zeros can be used together to implement Gosper's loop-detection algorithm, [54] which can find the period of a function of finite range using limited resources ...
Elements of the group have one s-electron in the outer electron shell. Hydrogen is not considered to be an alkali metal as it is not a metal, though it is more analogous to them than any other group. This makes the group somewhat exceptional. b The 14 f-block groups (columns) do not have a group number.
The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. [2] [3] Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.