# Log calculator

In mathematics and other exact sciences, logarithms are widely used - functions that are the inverse of raising to a power. For example, the logarithm of 10 of 1000 is equal to 3, since to obtain a thousand, 10 must be cubed, and the logarithm of 2 of 16 is equal to 4, since 16 is 2 to the fourth power.

Logarithms greatly simplify complex mathematical calculations, since they can be used to express exponentiation and root extraction as multiplication and division by the exponent.

In addition to logarithms, their inverse functions are also used in the exact sciences - antilogarithms, or “inverse logarithms”. The antilogarithm of x is the result of potentiation, or a number whose logarithm is equal to x.

Logarithms are denoted in formulas as log, and antilogarithms are denoted as ant log. These designations can be found not only in logarithmic tables, but also on the keyboards of engineering calculators. But today, to calculate these functions, special online calculators are more often used - much more convenient and accessible.

## The history of logarithms

Although the logarithmic function was invented much later, the prerequisites for its appearance were traced back to Antiquity. For example, the ancient Greek scientist Archimedes in the 3rd century BC established a connection between arithmetic and geometric progression, and investigated the properties of powers with natural exponents.

But tables of integer exponents (for bases 2, 3 and 4), which can be called logarithms in their modern sense, were obtained only in the 8th century - by the Indian scientist Virasena.

As astronomy and navigation developed, an increasingly urgent need arose to simplify complex mathematical calculations: multiplying and dividing multi-digit numbers, extracting roots, raising to powers.

In 1544, the German scientist Michael Stiefel took a decisive step in this direction by compiling a logarithmic table that was later named after him. The idea of comparing arithmetic and geometric progressions using tables was described by Stiefel in the book Arithmetica integra, and formed the basis for subsequent works by Nikolai Oresme and Nicola Chuquet.

In addition to them, the Scottish mathematician John Napier studied logarithms, who published Mirifici Logarithmorum Canonis Descriptio in Latin in 1614. This work described not only the properties of the logarithmic function, but also eight-digit tables of logarithms of sines, cosines and tangents. According to one version, it was Knepper who approved the name “logarithm”, which since the 17th century has become the only one and has no alternative.

Despite his serious contributions to science, John Knepper made a number of errors when compiling logarithmic tables (for numbers after the sixth digit), and they were disputed in 1620-1624.

In 1624, Johannes Kepler published his version of the logarithmic tables Chilias logarithmorum ad totidem numeros rotundos, and Edmund Wingate and William Oughtred invented the first slide rule. The British scientist Henry Briggs also carried out parallel research, and in 1617 he compiled 14-digit tables of decimal logarithms.

As in the case of Knepper's work, errors were also subsequently discovered in Briggs' tables. Initially, the table described decimal logarithms from 1 to 1000 with 8 decimal places, but after recalculation their number increased to 14 decimal places. In 1783, Georg Vega published a revised version, and on its basis the Bremiker tables were compiled - absolutely accurate and error-free.

It was the ready-made tables of logarithms that made this mathematical function so widespread and in demand. After all, now, instead of complex calculations, it was enough to check the required column and instantly get the desired result. The French mathematician Pierre-Simon Laplace said that the invention of logarithms “by shortening the astronomer’s work, doubled his life.”

In the 19th century, logarithms began to be used in complex analysis. In particular, Carl Friedrich Gauss in 1811 developed a theory of the multivaluedness of the logarithmic function, defined as the integral of 1/z. And Georg Friedrich Bernhard Riemann built a general theory of Riemann surfaces based on logarithms.

Today logarithms are used in algebra, geometry, physics, astronomy, engineering, economics and many other sciences. If earlier these functions were calculated manually or using logarithmic tables, and at the turn of the 20th-21st centuries - with the help of engineering calculators, today computer technology is used for this purpose. Just run the appropriate online calculator, and it will calculate the logarithm in a split second!