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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.
The function D(z) is sometimes called the Bloch-Wigner function. [1] Lobachevsky's function and Clausen's function are closely related functions. William Spence , after whom the function was named by early writers in the field, was a Scottish mathematician working in the early nineteenth century. [ 2 ]
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.
If different species occur in the octanol-water system by dissociation or association, several P-values and one D-value exist for the system. If, on the other hand, the substance is only present in a single species, the P and D values are identical. P is usually expressed as a common logarithm, i.e. Log P (also Log P ow or, less frequently, Log ...
The logarithm of the Euler function is the sum of the logarithms in the product expression, each of which may be expanded about q = 0, yielding (()) = =, which is a Lambert series with coefficients -1/n. The logarithm of the Euler function may therefore be expressed as
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.
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...
A model compound for the lipophilic cellular membrane is 1-octanol (a lipophilic medium-chain fatty alcohol), so the logarithm of the octanol-water partition coefficient, known as LogP, is used to predict the solubility of a potential oral drug. This coefficient can be experimentally measured or predicted computationally, in which case it is ...
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