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Log reduction is a measure of how thoroughly a decontamination process reduces the concentration of a contaminant. It is defined as the common logarithm of the ratio of the levels of contamination before and after the process, so an increment of 1 corresponds to a reduction in concentration by a factor of 10.
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.
What is often called a "log reduction" (technically a reduction by one order of magnitude) represents a 90% reduction in microbial population. Thus a process that achieves a "6-log reduction" (10 −6 ) will theoretically reduce an initial population of one million organisms to very close to zero.
Conversely, the measure is symmetric when the change decreases by an equivalent amount e.g. a halving is equal to a log 2 fold change of −1, a quartering is equal to a log 2 fold change of −2 and so on. This leads to more aesthetically pleasing plots, as exponential changes are displayed as linear and so the dynamic range is increased.
It is the number of degrees the temperature has to be increased to achieve a tenfold (i.e. 1 log 10) reduction in the D-value. The D-value of an organism is the time required in a given medium, at a given temperature, for a ten-fold reduction in the number of organisms.
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
Ampex tape recorders in the 1950s achieved 60 dB in practical usage, [26] In the 1960s, improvements in tape formulation processes resulted in 7 dB greater range, [28]: 158 and Ray Dolby developed the Dolby A-Type noise reduction system that increased low- and mid-frequency dynamic range on magnetic tape by 10 dB, and high-frequency by 15 dB ...
The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator Logarithms are easy to compute in some cases, such as log 10 (1000) = 3 . In general, logarithms can be calculated using power series or the arithmetic–geometric mean , or be retrieved from a precalculated logarithm table that provides a fixed precision.