Editing Logarithmic scale (section)

== Graphic representation ==
<!-- This section is linked from [[Order of magnitude]] -->
[[File:Logarithmic Scales-mkII.svg|thumb|upright=1.7|Various scales: lin–lin, [[Lin–log graph|lin–log, log–lin]], and [[Log–log plot|log–log]]. Plotted graphs are: ''y''&nbsp;=&nbsp;10<sup>&nbsp;''x''</sup> (<span style="color:red;">red</span>), ''y''&nbsp;=&nbsp;''x'' (<span style="color:green;">green</span>), ''y''&nbsp;=&nbsp;log<sub>''e''</sub>(''x'') (<span style="color:blue;">blue</span>).]]

The top left graph is linear in the X- and Y-axes, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y-axis of the bottom left graph, and the Y-axis ranges from 0.1 to 1000.

The top right graph uses a log-10 scale for just the X-axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y-axis.

Presentation of data on a logarithmic scale can be helpful when the data:
* covers a large range of values, since the use of the logarithms of the values rather than the actual values reduces a wide range to a more manageable size;
* may contain [[exponential law]]s or [[power law]]s, since these will show up as straight lines.

A [[slide rule]] has logarithmic scales, and [[nomogram]]s often employ logarithmic scales. The [[geometric mean]] of two numbers is midway between the numbers. Before the advent of computer graphics, logarithmic [[graph paper]] was a commonly used scientific tool.

=== Log–log plots ===
{{Main|Log–log plot}}
[[File:2010- Decreasing renewable energy costs versus deployment.svg|thumb|upright=1.3|A log–log plot condensing information that spans more than one order of magnitude along both axes]]
If both the vertical and horizontal axes of a plot are scaled logarithmically, the plot is referred to as a [[log–log plot]].

=== Semi-logarithmic plots ===
{{Main|Semi-log plot}}
If only the [[ordinate]] or [[abscissa]] is scaled logarithmically, the plot is referred to as a [[semi-logarithmic]] plot.

=== Extensions ===
A modified log transform can be defined for negative input (''y'' < 0) to avoid the singularity for zero input (''y'' = 0), and so produce symmetric log plots:<ref name="Webber2012">{{cite journal | last=Webber | first=J Beau W | title=A bi-symmetric log transformation for wide-range data | journal=Measurement Science and Technology | publisher=IOP Publishing | volume=24 | issue=2 | date=2012-12-21 | issn=0957-0233 | doi=10.1088/0957-0233/24/2/027001 | page=027001| s2cid=12007380 | url=https://kar.kent.ac.uk/32810/2/2012_Bi-symmetric-log-transformation_v5.pdf }}</ref><ref name="Matplotlib 3.4.2 documentation 2021">{{cite web | title=Symlog Demo | website=Matplotlib 3.4.2 documentation | date=2021-05-08 | url=https://matplotlib.org/stable/gallery/scales/symlog_demo.html | access-date=2021-06-22}}</ref>
:<math>Y=\sgn(y)\cdot\log_{10}(1+|y/C|)</math>
for a constant ''C''=1/ln(10).