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In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution, from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
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.
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.
Example Bjerrum plot: Change in carbonate system of seawater from ocean acidification.. A Bjerrum plot (named after Niels Bjerrum), sometimes also known as a Sillén diagram (after Lars Gunnar Sillén), or a Hägg diagram (after Gunnar Hägg) [1] is a graph of the concentrations of the different species of a polyprotic acid in a solution, as a function of pH, [2] when the solution is at ...
In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, ( (), ordinate axis) plotted against reciprocal of the temperature (/, abscissa). [1] Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions.
The Bode phase plot is the graph of the phase, commonly expressed in degrees, of the argument function ((=)) as a function of . The phase is plotted on the same logarithmic ω {\displaystyle \omega } -axis as the magnitude plot, but the value for the phase is plotted on a linear vertical axis.