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A serial dilution is the step-wise dilution of a substance in solution, either by using a constant dilution factor, or by using a variable factor between dilutions. If the dilution factor at each step is constant, this results in a geometric progression of the concentration in a logarithmic fashion.
Demonstrating log* 4 = 2 for the base-e iterated logarithm. The value of the iterated logarithm can be found by "zig-zagging" on the curve y = log b (x) from the input n, to the interval [0,1]. In this case, b = e. The zig-zagging entails starting from the point (n, 0) and iteratively moving to (n, log b (n) ), to (0, log b (n) ), to (log b (n ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:
Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a. In arithmetic modulo an integer m , the more commonly used term is index : One can write k = ind b a (mod m ) (read "the index of a to the base b modulo m ") for b k ≡ a (mod m ) if k is a primitive ...
The logarithmic decrement can be obtained e.g. as ln(x 1 /x 3).Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain.. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]
This was considered a minor step compared to the others for smaller discrete log computations. However, larger discrete logarithm records [ 1 ] [ 2 ] were made possible only by shifting the work away from the linear algebra and onto the sieve (i.e., increasing the number of equations while reducing the number of variables).