__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 10

^{3}is 1000 i.e. 10^{3}= 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

10

^{2}= 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. 2

^{3}= 8