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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/01/17 02:18:37」(JST)

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The log-lin type of a semi-log graph, defined by a logarithmic scale on the y-axis, and a linear scale on the x-axis. Plotted lines are: y = 10^x (red), y = x (green), y = log(x) (blue).

The lin-log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10^x (red), y = x (green), y = log(x) (blue).

In science and engineering, a semi-log graph or semi-log plot is a way of visualizing data that are related according to an exponential relationship. One axis is plotted on a logarithmic scale. This kind of plot is useful when one of the variables being plotted covers a large range of values and the other has only a restricted range – the advantage being that it can bring out features in the data that would not easily be seen if both variables had been plotted linearly.^[1]

All equations of the form form straight lines when plotted semi-logarithmically, since taking logs of both sides gives

This can easily be seen as a line in slope-intercept form with as the slope and as the vertical intercept. To facilitate use with logarithmic tables, one usually takes logs to base 10 or e, or sometimes base 2:

The term log-lin is used to describe a semi-log plot with a logarithmic scale on the y-axis, and a linear scale on the x-axis. Likewise, a lin-log plot uses a logarithmic scale on the x-axis, and a linear scale on the y-axis. Note that the naming is output-input (y-x), the opposite order from (x, y).

On a semi-log plot the spacing of the scale on the y-axis (or x-axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on lin-lin scales. A log-log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.

Equations

The equation for a line with an ordinate axis logarithmically scaled would be:

The equation of a line on a plot where the abscissa axis is scaled logarithmically would be

Real-world examples

Phase diagram of water

In physics and chemistry, a plot of logarithm of pressure against temperature can be used to illustrate the various phases of a substance, as in the following for water:

Log-lin pressure–temperature phase diagram of water. The Roman numerals indicate various ice phases.

2009 "swine flu" progression

While ten is the most common base, there are times when other bases are more appropriate, as in this example:

A semi-logarithmic plot of cases and deaths in the 2009 outbreak of influenza A (H1N1). Notice that while the horizontal (time) axis is linear, with the dates evenly spaced, the vertical (cases) axis is logarithmic, with the evenly spaced divisions being labelled with successive powers of two.

Microbial growth

In biology and biological engineering, the change in numbers of microbes due to asexual reproduction and nutrient exhaustion is commonly illustrated by a semi-log plot. Time is usually the independent axis, with the logarithm of the number or mass of bacteria or other microbe as the dependent variable. This forms a plot with four distinct phases, as shown below.

Bacterial growth curve

References

^ M. Bourne Graphs on Logarithmic and Semi-Logarithmic Paper (www.intmath.com)

English Journal

[Excitation and relaxation of metastable state NaK(1 3pi) at high vibrational levels].

Luan NN, Cai Q, Zhang LP, Dai K, Shen YF.SourceSchool of Physics Science and Technology, Xinjiang University, Urumqi 830046, China.
Guang pu xue yu guang pu fen xi = Guang pu.Guang Pu Xue Yu Guang Pu Fen Xi.2011 Nov;31(11):2919-22.
The authors have investigated collision vibrational energy transfer rate constants in NaK[1 3pi(v)] and He system. Pump laser excitation of the spin-forbidden band was used to produce very highly vibrationally excited metastable state NaK[1 3pi (v = 22, 21, 20)]. The probe laser was used to excite t
PMID 22242485

The gender earnings gap among pharmacists.

Carvajal MJ, Armayor GM, Deziel L.SourceDepartment of Sociobehavioral and Administrative Pharmacy, Nova Southeastern University College of Pharmacy, 3200 S. University Drive, Fort Lauderdale, FL 33328, USA.
Research in social & administrative pharmacy : RSAP.Res Social Adm Pharm.2011 Sep 27. [Epub ahead of print]
BACKGROUND: A gender earnings gap exists across professions. Compared with men, women earn consistently lower income levels. The determinants of wages and salaries should be explored to assess whether a gender earnings gap exists in the pharmacy profession.OBJECTIVES: The objectives of this study we
PMID 21958465

Japanese Journal

Hyundai Steel's Ramp-up Strategy and the Learning Effect

Annals of Business Administrative Science 15(4), 163-174, 2016
NAID 130005169836

Hyundai Steels Ramp-up Strategy and the Learning Effect

Annals of Business Administrative Science advpub(0), 2016
NAID 130005166384

Markedly Different Rise and Fall Times in Transient Electroluminescence of 4,4$'$-N,N$'$-Dicarbazolylbiphenyl:fac-Tris(2-phenylpyridinate) Iridium(III)-Based Organic Light Emitting Diodes