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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.
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then
The dilution in welding terms is defined as the weight of the base metal melted divided by the total weight of the weld metal. For example, if we have a dilution of 0.40, the fraction of the weld metal that came from the consumable electrode is 0.60.
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]
The distribution coefficient, log D, is the ratio of the sum of the concentrations of all forms of the compound (ionized plus un-ionized) in each of the two phases, one essentially always aqueous; as such, it depends on the pH of the aqueous phase, and log D = log P for non-ionizable compounds at any pH.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
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In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.