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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).
The name of the function includes a special prefix 'c:', which causes AutoCAD to recognize the function as a regular command. The user, upon typing 'pointlabel' at the AutoCAD command line, would be prompted to pick a point, either by typing the X and Y coordinates, or clicking a location in the drawing.
In the lower plot, both the area and population data have been transformed using the logarithm function. In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point z i is replaced with the transformed value y i = f(z i), where f is a function.
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact that the convolution of two log-concave functions is log-concave.
As of AutoCAD 2007 and later, AutoLISP or Visual-LISP programs can call routines written in Visual Studio .NET (VB or C#). Programmers can now create dialogs in VB or C# that have the full range of controls found in the .NET Forms API and can be called and accessed from Visual-LISP.
The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln(x) around the z-axis. In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related:
As discussed above, the function log b is the inverse to the exponential function . Therefore, their graphs correspond to each other upon exchanging the x - and the y -coordinates (or upon reflection at the diagonal line x = y ), as shown at the right: a point ( t , u = b t ) on the graph of f yields a point ( u , t = log b u ) on the graph of ...