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LogarithmsBy

10 th classNarayana Techno School

KKD- RRPet

What are logarithms

The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

For exampleThe logarithm of 10000 to base 10 is 3, because 10 to the power 4 is 10000: 10000 = 10 × 10 × 10 × 10 = 104

History

Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations.

The logarithm of a positive real number x with respect to base b is the exponent by which b must be raised to yield x.

Definition:

log b x = y

For example: log 100 =2 i.e., log10100 = 2

The logarithm to base 10 (b = 10) is called the common logarithm and has many applications in science and engineering.

Applications Logarithms have many applications inside and outside mathematics.Logarithms occur in several laws describing human perception in Psychology.

Natural logarithms are closely linked to counting prime numbers, an important topic in number theory.

Logarithms arise in probability theory.

Logarithms are related to musical tones and intervals.

Logarithms occur in definitions of the dimension of fractals.

Logarithms are useful in many ways.

They were rapidly adopted by navigators, scientists,

engineers, and others to perform computations more

easily.