Logarithm

About Logarithm:

Logarithm means in mathematics, logarithm of a number is the exponent to which another fixed value; the base should be raised to produce to that number. 

For example: Logarithm of 1000 to base 10 is 3, because 10³ is 1000 i.e. 10³ = 10 × 10 × 10 = 1000. Usually, for any two real numbers b and x where b is positive and b ≠ 1,

y=bx⇔x=logb(y)

The logarithm of base 10 (b = 10) is called the common logarithm and have a lot of applications in engineering and science. The natural logarithms have the irrational (transcendental) number e (≈ 2.718) as its base; logarithm use is widespread in wholesome mathematics, mainly in calculus. The logarithm in binary (binary logarithm) is uses base 2 (b = 2) and is prominent in computer science.

Logarithms were introduced by “John Napier” in the early on 17th century as a means to simplify computations. They were quickly adopted by scientists, engineers, navigators and others to perform calculations more easily, by slide rules and logarithm tables. Dreary multi digit multiplication steps able to be replaced by table look-ups and simpler adding up because of the truth important in its own right that the logarithm of a product is the sum of the logarithms of the factors:

logb(xy)=logb(x)+logb(y),

Provided that the b, x and y are all positive and b ≠ 1. Now a day’s notion of logarithms comes from “Leonhard Euler”, who associated them to the exponential function in 18th century.

Logarithmic scales reduce wide range of quantities to smaller scopes. For ex: the decibel is the logarithmic unit quantifying signal power ratios and amplitude. In chemistry subject, pH is a logarithmic measure for acidity of aqueous solution. Logarithms are general place in scientific formulas, in measurements of the complexity of algorithms and of geometric objects are called fractals. They clarify musical intervals, come into view in formula counting prime numbers, a few models in psychophysics, and could aid in forensic tasks.

In the similar method the logarithm overturn exponentiation, the complex logarithm is opposite function of the exponential function applied to complex number. The discrete logarithm is a different variant; it has applications in public-key cryptography.

In other words logarithm means:

A logarithm is the power of to which a number have to be raised in order to get another number. For ex, the base 10 logarithm of 100 is 2, because 10 rose to the power of 2 is 100:

log 100 = 2

because

10² = 100

This is an example of a base 10 logarithm. We can name it a base ten logarithm because 10 is the number that is raised to a power. The base unit is the number is raised to a power. There are logarithms using differ base units. You can use 2 as a base unit. For instance, the base 2 logarithm of 8 is 3, because 2 rise to the power of 3 equals 8.

Log2 of 8 = 3

I.e. 2³ = 8