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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/06/13 15:46:11」(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 graph 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 graph 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 graph uses the logarithmic scale for both axes, and hence is not a semi-log graph.

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

Quebec Trophoblastic Disease Registry: How to Make an Easy-To-Use Dynamic Database.

Sauthier P1, Breguet M, Rozenholc A, Sauthier M.
International journal of gynecological cancer : official journal of the International Gynecological Cancer Society.Int J Gynecol Cancer.2015 May;25(4):729-733.
OBJECTIVE: To create an easy-to-use dynamic database designed specifically for the Quebec Trophoblastic Disease Registry (RMTQ).INTRODUCTION: It is now well established that much of the success in managing trophoblastic diseases comes from the development of national and regional reference centers.
PMID 25675044

A controlled microfluidic electrochemical lab-on-a-chip for label-free diffusion-restricted DNA hybridization analysis.

Ben-Yoav H1, Dykstra PH2, Bentley WE3, Ghodssi R4.
Biosensors & bioelectronics.Biosens Bioelectron.2015 Feb 15;64:579-85. doi: 10.1016/j.bios.2014.09.069. Epub 2014 Oct 11.
Lab-on-a-chip (LOC) devices for electrochemical analysis of DNA hybridization events offer a technology for real-time and label-free assessment of biomarkers at the point-of-care. Here, we present a microfluidic LOC, with 3 × 3 arrayed electrochemical sensors for the analysis of DNA hybridization e
PMID 25310492

Coupling of g proteins to reconstituted monomers and tetramers of the M2 muscarinic receptor.

Redka DS1, Morizumi T2, Elmslie G3, Paranthaman P1, Shivnaraine RV1, Ellis J4, Ernst OP5, Wells JW6.
The Journal of biological chemistry.J Biol Chem.2014 Aug 29;289(35):24347-65. doi: 10.1074/jbc.M114.559294. Epub 2014 Jul 14.
G protein-coupled receptors can be reconstituted as monomers in nanodiscs and as tetramers in liposomes. When reconstituted with G proteins, both forms enable an allosteric interaction between agonists and guanylyl nucleotides. Both forms, therefore, are candidates for the complex that controls sign
PMID 25023280