The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published …

History and use. The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. The table produced by the Indian mathematician Āryabhaṭa …

Since the bases of the logs are the same and the logarithms are added, the arguments can be multiplied together. We then simplify the right side of the equation: The logarithm can be converted to exponential form: Factor the equation: Although there are two solutions to the equation, logarithms cannot be negative. Therefore, the only real ...

Here are some uses for Logarithms in the real world: Earthquakes. The magnitude of an earthquake is a Logarithmic scale. The famous "Richter Scale" uses this formula: M = log 10 A + B. Where A is the amplitude (in mm) measured by the Seismograph and B …

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8. In the same fashion, since 102 = 100, then 2 = log10 100. Logarithms of the latter sort (that is, …

Two kinds of logarithms are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number. The power to which the base e (e = 2.718281828.....) must be raised to obtain a number is called the natural logarithm (ln) of the …

Napier invented logarithms, Edmund Gunter invented the logarithmic scales (lines etched on metal or wood), but it was William Oughtred, in England who invented the sliderule. Using the concept of Napier’s bones, he inscribed logarithms on strips of wood and invented the calculating "machine" which was used up until the mid-1970s when the ...

Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) …

Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables.The technique is used for both hypothesis testing and model building. In both these uses, models are tested to find the most parsimonious (i.e., least complex) model that best accounts for the variance in the observed frequencies.