uses of logarithms

3. 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.

4. For example
The logarithm of 10000 to base 10 is 3, because 10 to the
power 4 is 10000: 10000 = 10 × 10 × 10 × 10 = 104

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

6. 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.
log b x = y

7. The logarithm to base 10 (b = 10) is called the
common logarithm and has many applications in
science and engineering.
For example:
log 100 =2
i.e., log10100 = 2

8. 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.

9. 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.