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The linear–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 plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale.
A logarithmic unit is a unit that can be used to express a quantity (physical or mathematical) on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the ...
Download as PDF; Printable version; ... El Gamal discrete log cryptosystem; ... Logarithmic form; Logarithmic graph paper; Logarithmic growth;
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
As the common log of ten is one, of a hundred is two, and a thousand is three, the concept of common logarithms is very close to the decimal-positional number system. The common log is said to have base 10, but base 10,000 is ancient and still common in East Asia.
Log probabilities make some mathematical manipulations easier to perform. Optimization. Since most common probability distributions —notably the exponential family —are only logarithmically concave , [ 2 ] [ 3 ] and concavity of the objective function plays a key role in the maximization of a function such as probability, optimizers work ...
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For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d. Derivations also use the log definitions x = b log b (x ...