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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.
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 ...
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
Three main logarithmic dilution scales are in regular use in homeopathy. Hahnemann created the "centesimal" or "C scale", diluting a substance by a factor of 100 at each stage. There is also a decimal dilution scale (notated as "X" or "D") in which the preparation is diluted by a factor of 10 at each stage. [9]
A logarithmic unit is a unit that can be used to express a quantity (physical or mathematical) on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the ...
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.
The actual formula for calculating a dog's age, it turns out, might mean breaking out your graphing calculator. ... 16 x ln( the natural logarithm of your dog’s age in "human years") + 31.
The following formulas can be used to calculate the volumes of solute (V solute) and solvent (V solvent) to be used: [1] = = where V total is the desired total volume, and F is the desired dilution factor number (the number in the position of F if expressed as "1/F dilution factor" or "xF dilution"). However, some solutions and mixtures take up ...