A logarithmic scale is a system of graduation on a half-line particularly adapted to give an account of the orders of magnitude in the applications. Moreover it makes it possible to make available a broad range from values. Definition of the logarithmic scale The logarithmic scale of a half-line is determined by the data of a point '' has '' this half-line. For any point '' M '' of ['' OX ''), the vectors \ vec OA and \ vec OM are positively colinéaires. There thus exists a single reality '' R '' such as: \vec{OM}=r.\vec{OA}. The coordinated ''' logarithmic curve ''' of '' M '' is given by: : \ log {R} In particular, the coordinate logarithmic curve of has is log (1) =0. It is the origin of the reference mark. In this formula, the logarithmic curve can indicate: In mathematics, the Napierian logarithm, primitive of 1/x. In statistics, generally the decimal logarithm. In data processing, the binary logarithm. the distance which separates 1 from 10 is the same one as that which separate 10 from 100 and that which separates 0,1 from 1 because log (100) - log (10) = log (10) - log (1) = log (1) - log (0,1). Each one of these intervals is called a module. the distance which separates 1 from 2 is equal to that which separates 10 from 20 but is higher than that which separates 2 from 3 because log (2) - log (1) = log (20) - log (10) > log (3) - log (2). That induces a kind of recurring irregularity in the graduations. Example of logarithmic scale to three modules The logarithmic scale is an alternative on a linear scale. It can prove to be preferable for two reasons: Situation 1: When one studies a phenomenon using a wide range of values, the linear scale is badly adapted. One prefers to him a scale logarithmic curve which spaces the low values and brings closer the strong values. Situation 2: Certaines feelings follows the Loi of Weber-Fechner which affirms that they can “ grow like the logarithm of exciting .” The logarithmic scale then gives a faithful reflection of subjective perception. Graphic observation Attention, with differentiating ln well and log which allow both to create logarithmic scales but calculations of slope will be different. The diagram above makes it possible to visualize the two types of scales: For the linear scale , two graduations of which the difference is worth 10 is remotely constant. For the scale logarithmic curve , two graduations whose report/ratio is worth 10 are remotely constant. Examples Magnitude of a seism pH Magnitude of the stars Music Its semi-logarithmic Reference mark, Reference mark log-log Simple: Logarithmic scale Random links:Belpberg | Traudl Junge | Stenotomus | Michel Combes (military) | Hydrastis canadensis
The logarithmic scale of a half-line is determined by the data of a point '' has '' this half-line. For any point '' M '' of ['' OX ''), the vectors \ vec OA and \ vec OM are positively colinéaires. There thus exists a single reality '' R '' such as: \vec{OM}=r.\vec{OA}. The coordinated ''' logarithmic curve ''' of '' M '' is given by: : \ log {R} In particular, the coordinate logarithmic curve of has is log (1) =0. It is the origin of the reference mark.
In this formula, the logarithmic curve can indicate:
That induces a kind of recurring irregularity in the graduations.
The logarithmic scale is an alternative on a linear scale. It can prove to be preferable for two reasons:
Situation 1: When one studies a phenomenon using a wide range of values, the linear scale is badly adapted. One prefers to him a scale logarithmic curve which spaces the low values and brings closer the strong values.
Situation 2: Certaines feelings follows the Loi of Weber-Fechner which affirms that they can “ grow like the logarithm of exciting .” The logarithmic scale then gives a faithful reflection of subjective perception.
Attention, with differentiating ln well and log which allow both to create logarithmic scales but calculations of slope will be different.
The diagram above makes it possible to visualize the two types of scales:
Simple: Logarithmic scale
