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Logarithms in mathematics are one of the most difficult lessons in

 mathematics. We will  learn this lesson  In an easy and simple

 way. We will give a full explanation of this  lesson,  which includes

 what  it is Logarithms, what is their definition, characteristics,

 history, rules, formulas and  types. You will get to know it

 all  And more on the Math page in English

What are logarithms 

Just logarithms for numbers somewhere in the range of 0 and

10 were normally remembered for logarithm tables. To acquire the logarithm of some number outside of this reach, the

number was first written in logical documentation as the result of its huge digits and its outstanding force—for instance, 358

would be composed as 3.58 × 102, and 0.0046 would be

composed as 4.6 × 10−3. At that point the logarithm of the critical digits—a decimal portion somewhere in the range of 0

and 1, known as the mantissa. For instance, to discover the logarithm of 358, one would look into log 3.58 ≅ 0.55388.

Hence, log 358 = log 3.58 + log 100 = 0.55388 + 2 = 2.55388.

In the case of a number with a negative example, for example, 0.0046, one would look into

log 4.6 ≅ 0.66276. Subsequently, log 0.0046 = log 4.6 + log 0.001 = 0.66276 − 3 = −2.33724

History of logarithms

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substances.

Buy in Now History of logarithms The innovation of

logarithms was foreshadowed by the correlation of math and

mathematical arrangements.

In a mathematical arrangement each term shapes a

consistent proportion with its replacement; for instance, … 1/1,000, 1/100, 1/10, 1, 10, 100, 1,000… has a typical

proportion of 10.

In a number-crunching arrangement each progressive term

contrasts by a consistent, known as the normal distinction; for

instance, … −3, −2, −1, 0, 1, 2, 3 … has a typical distinction of

1. Note that a mathematical succession can be written as far

as its basic proportion; for the model mathematical

arrangement given previously: … 10−3, 10−2, 10−1, 100,

101, 102, 103… . Duplicating two numbers in the

mathematical succession, say 1/10 and 100, is equivalent to

adding the related examples of the normal proportion, −1 and

2, to get 101 = 10.

Accordingly, increase is changed into expansion. The first

correlation between the two arrangements, be that as it may,

did not depend on any unequivocal

utilization of the remarkable documentation; this was a later

turn of events. In 1620 the principal table dependent on the idea of relating mathematical and number-crunching

arrangements was distributed in Prague by the Swiss mathematician Joost Bürgi.

The Scottish mathematician John Napier distributed his revelation of logarithms in 1614.

His

motivation was to aid the augmentation of amounts that were then called sines.

The entire sine was the worth of the side of a right-calculated triangle with a huge hypotenuse. (Napier'sunique hypotenuse

was 107.) His definition was given as far as relative rates.The logarithme, in this way, of any sine is a number neerely

communicating the line which expanded similarly in the

meene time whiles the line of the entire sine diminished relatively into that sine, the two movements being equivalent

planned and the start similarly shift.

In collaboration with the English mathematician Henry Briggs,

Napier changed his logarithm into its advanced structure.

For the Naperian logarithm the correlation would be between

focuses proceeding onward a graduated straight line, the L point (for the logarithm) moving consistently from short

boundlessness to in addition to endlessness, the X point (for the sine) moving from zero to vastness at a speed relative to

its separation from nothing. Moreover, L is zero when X is one and their speed is equivalent now.

The pith of Napier's disclosure is that this establishes a

speculation of the connection between the number-crunching

and mathematical arrangement; i.e., augmentation and raising to a force of the upsides of the X point relate to expansion and

duplication of the upsides of the L point, individually.Practically speaking it is advantageous to restrict the L and X movement

by the prerequisite that L = 1 at X = 10 notwithstanding the condition that X = 1 at L = 0. This change delivered the

Briggsian, or normal, logarithm. Napier passed on in 1617 and Briggs proceeded alone, distributing in 1624 a table of

logarithms determined to 14 decimal spots for numbers from 1 to 20,000 and from 90,000 to 100,000.

In 1628 the Dutch distributor Adriaan Vlacq drew out a 10-

place table for values from 1 to 100,000, adding the missing

70,000 qualities. Both Briggs and Vlacq occupied with setting up log geometrical tables.

Such early tables were either to the 100th of a degree or to

one moment of curve. In the eighteenth century, tables were distributed for 10-second spans, which were helpful for seven-

decimal-place tables. As a rule, better stretches are needed for figuring logarithmic elements of more modest numbers for

instance, in the computation of the capacities log sin x and log tan x.

The accessibility of logarithms incredibly affected the type of plane and circular geometry.

The response to the tables at that point consisted of just two stages, getting logarithms and, subsequent to performing

calculations with the logarithms, acquiring antilogarithms.

Properties of logarithms

Logarithms have the following properties (where b in all properties is the basis of the logarithm)

• Lo b 1 = 0, because raising any number to the power of zero is equal to 1; That is, b 0 = 1.
• lobe b = 1, because raising any number to the power of one is the same number; That is, b 1 = b.
• Lob bx = x, and in general, lo b b q (x) = q (x).
• Lob bx = x, and in general, lo b b q (x) = q (x).
• Lob (x * y) = lop x + lop y.
• lob (x / y) = lob x - lob y.
• Loop 0 = an undefined value, because the result of any number when raising it to an exponent cannot be zero
• Inverting the logarithm, i.e. making its numerator the place of its denominator, and its denominator the place of its numerator, or vice versa, switching the base, and the result
• The value of both decimal and natural logarithms can be calculated with a calculator, so the logarithm basis of the Niperian number or the number 10 can be changed; To make it easier to calculate using a calculator by changing the base property, which states that: lobe x = lop x/ lobe a; Where B = 10, or the Nepali number (E), and this can be illustrated by the following example:

Types of logarithms

There are several types of logarithms, depending on the value of the

 base, which differs greatly between them, but there are two types of

 logarithms that are more common than others, and they can also be

 calculated using all types of calculators, and the following is an explanation of each of them:

• Decimal logarithm: It is the most common, and it is the logarithm whose base is the number 10, and often the base is not written in this type so that the reader automatically deduces that the base here is 10; That is: Lu 10 x = Lu x
• Natural Logarithm: It is the logarithm whose base is the Nibrian number (E), and it is written in the following form: Luh Q,