logarithm

(noun)

for a number $x$, the power to which a given base number must be raised in order to obtain $x$

Related Terms

Examples of logarithm in the following topics:

  • Statistical Literacy

    • Many financial web pages give you the option of using a logarithmic Y-axis.
    • What would result in a straight line with the logarithmic option chosen?

  • Logarithms

    • There is a base which results in "natural logarithms" and that is called e and equals approximately 2.718.
    • Natural logarithms can be indicated either as: $\text{ln}(x)$ or $\text{log}_e(x)$
    • Taking the antilog of a number simply raises the base of the logarithm in question to that number.

  • Box-Cox Transformations

    • In the bottom row (on a semi-logarithmic scale), the choice λ = 0 corresponds to a logarithmic transformation, which is now a straight line.
    • We superimpose a larger collection of transformations on a semi-logarithmic scale in Figure 2.
    • Economists often analyze the logarithm of income corresponding to λ = 0; see Figure 4.

  • Poisson Distribution

  • Tukey Ladder of Powers

    • For the US population, the logarithmic transformation applied to y makes the relationship almost perfectly linear.
    • The logarithmic transformation corresponds to the choice λ = 0 by Tukey's convention.
    • The logarithmic fit is in the upper right frame when λ = 0.
    • It is clear that the logarithmic transformation (λ = 0) is nearly optimal by this criterion.
    • Indeed, the growth of population in Arizona is logarithmic, and appears to still be logarithmic through 2005.

  • Transforming data (special topic)

    • For instance, a plot of the natural logarithm of player salaries results in a new histogram in Figure 1.28(b).
    • Transformations other than the logarithm can be useful, too.

  • Log Transformations

  • When to Use These Tests

    • For example, if we are working with data on peoples' incomes in some currency unit, it would be common to transform each person's income value by the logarithm function.
    • However, following logarithmic transformations of both area and population, the points will be spread more uniformly in the graph .
    • In the lower plot, both the area and population data have been transformed using the logarithm function.

  • Odds Ratios

    • The logarithm of the odds ratio—the difference of the logits of the probabilities—tempers this effect and also makes the measure symmetric with respect to the ordering of groups.
    • For example, using natural logarithms, an odds ratio of $\frac{36}{1}$ maps to $3.584$, and an odds ratio of $\frac{1}{36}$ maps to $−3.584$.

  • Additional Measures of Central Tendency

    • The geometric mean has a close relationship with logarithms.