Logarithm: how to calculate?

degree of individual numbers is a mathematical term coined centuries ago.In geometry and algebra there are two options - decimal and natural logarithms.They are calculated by different formulas, while equations differing writing is always equal to each other.This identity characteristic properties which are useful potential function.

Features and important features

Currently distinguish ten known mathematical skills.The most common and popular of them are:

  • Podkoren log, divided by the value of the root is always the same as the logarithm √.
  • Artwork log always equal to the sum of the manufacturer.
  • Lg = largest extent by multiplying the number of which it is built.
  • If you take the log of the dividend the divisor will lg private.

In addition, there is an equation based on the main identity (considered a key), the transition to the updated base and several minor formulas.

Calculating the logarithm - a rather specific task, therefore to the integration of properties in the solution must be a

pproached carefully and regularly check their actions and consistency.We should not forget about the tables, which need to constantly consult and be guided only by the data found there.

Species mathematical term

main differences of the mathematical number of "hidden" at the bottom (a).If it has a value of 10, that is the decimal log.Otherwise, «a» is converted to a "y" and has a transcendental and irrational features.It is also worth noting that the actual value is calculated by special equation where evidence becomes theory studied beyond high school curriculum.

decimal logarithms of the type widely used in the calculation of complex formulas.Compiled entire tables facilitate the calculations and clearly showing the problem solving process.At the same time before the actual transition to the business needs to build a log in the standard form.In addition, each store school supplies you can find a special line with scale, helping to solve the equation of any complexity.Logarithm of Briggovym called, or a number of Euler, in honor of the explorer who first published value and found the opposition of the two definitions.

Two types of formula

All types and varieties of tasks on calculation of the response, with the term provided in the log, have a separate name and rigorous mathematical device.An exponential equation is an almost exact copy of logarithmic calculations, when viewed from the correct solution.Just the first option includes a number of specialized, help you quickly understand the condition and replaces the second log on ordinary degree.The calculations using the last formula should include a variable value.

difference and terminology

Both main index have their own distinguishing features of each other:

  • logarithm.An important part of - obligatory presence of a base.The standard version of magnitude 10. marking sequences - log x or lg x.
  • Natural.If his base is a sign «e», which is a constant that is strictly identical to the calculated equation, where n is rapidly moving toward infinity, the approximate size of the digital equivalent of 2.72.Official marks, adopted both in school and in a more complex professional formulas, - ln x.
  • different.In addition to basic logarithms meet hex and binary types (base 16 and 2, respectively).There are complex version with baseline 64, is subject to the systematic control of adaptive type, with geometric precision calculation produces the final result.

terminology includes the following quantities in algebraic problem:

  • value;
  • argument;
  • basis.

Calculation of log

There are three ways to quickly and orally to make all the necessary calculations to find a result with interest must be the result of the decision.Initially approximate logarithm your order (scientific record of the number of degree).Every positive value can be set by the equation, where it will be equal to the mantissa (number from 1 to 9), multiplying by ten to the n-th degree.This option is based on the count of two mathematical facts:

  • the product and the amount of log always have the same rate;
  • logarithm taken of the numbers from one to ten, can not exceed the value of 1 point.
  1. If an error in the calculation does occur, it is never less than one in the direction of subtraction.
  2. increased accuracy, given that the base three-lg is the final result - five-tenths of a unit.Therefore, any mathematical value of more than 3 automatically adds one point to the answer.
  3. Almost perfect accuracy is achieved if the hand is a specialized table that can be easily used in their evaluation activities.You can use it to figure out what is the common logarithm of up to ten percent of the original number.

real history log

sixteenth century keenly felt the need for more complex terms than has been known to science at the time.This was especially true of division and multiplication of numbers with a large multi-valued sequence, including fractions.At the end of the second half of the era of multiple minds we came to the conclusion on the addition of numbers with the help of the table, which compares the two progression: arithmetic and geometric.At the same time all basic calculations had to rest on the last value.Likewise, scientists have integrated and subtraction.

first mention of lg was held in 1614.It made an amateur mathematician by the name of Napier.It is worth noting that, despite the great popularization of the results obtained in the formula was a mistake due to ignorance of some of the definitions that appear later.It begins with the sixth sign of the index.The closest to an understanding of logarithms were brothers Bernoulli, and legitimizing debut occurred in the eighteenth century by Euler.He and distributed function in education.

comprehensive history log

Debut lg attempts to integrate into the broad masses did at the dawn of the 18th century, Bernoulli and Leibniz.But the integrity of theoretical calculations, they have not been able to make.On this occasion, the whole debate was conducted, but the exact definition of the number is given.Later, the dialogue has resumed, but between Euler and d'Alembert.The latter was, in principle, agree with a lot of facts offered by the founder of the magnitude, but believed that the positive and negative indicators must be equal.In mid-century, the formula has been demonstrated as a final option.In addition, Euler was published derivative of the logarithm and the first drawn graphics.

tables indicate the number of properties that are not multivalued figures can be multiplied, and find their log, and lay down by the special tables.

particularly valuable, this figure was for astronomers who are forced to work with a large set of sequences.In Soviet times logarithm sought in the collection Bradis, released in 1921.Later, in 1971, came the publication of Vega.