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The power law of practice states that the logarithm of the reaction time for a particular task decreases linearly with the logarithm of the number of practice trials taken. It is an example of the learning curve effect on performance.
A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usually increases with increased experience (the horizontal axis), that is to say, the more someone, groups, companies or industries perform a task, the better their performance at the task.
The logarithm expresses depth of "choice tree" hierarchy – log 2 indicates binary search was performed. Addition of 1 to n takes into account the "uncertainty about whether to respond or not, as well as about which response to make." [3] In the case of choices with unequal probabilities, the law can be generalized as:
Some learning consultants claim reviewing material in the first 24 hours after learning information is the optimum time to actively recall the content and reset the forgetting curve. [8] Evidence suggests waiting 10–20% of the time towards when the information will be needed is the optimum time for a single review.
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
Logarithmic can refer to: Logarithm, a transcendental function in mathematics; Logarithmic scale, the use of the logarithmic function to describe measurements;
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).
Logarithmic growth is the inverse of exponential growth and is very slow. [2] A familiar example of logarithmic growth is a number, N, in positional notation, which grows as log b (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic. [3] In more advanced mathematics, the partial sums of the harmonic series