## Logarithms - Introduction

What you will learn in Logarithms?

In exponents, how do we write 2 to the power of 3?
23 = 8.
In logarithms, how do we write logarithm of 8 to base 2?
log 2 8 = 3
If ax = n is exponential form, then
log a n = x is the logarithmic form.

#### This lesson will cover Logarithms in detail.

Or, if you wish to capture a terse overview of each Logarithm topic, then go through each of the following header-links. You can also click the header-links to take you to the page on the specific Logarithm topic.

Definition of Logarithm:
if 23 = 8, then log 2 8 = 3
if an = x, then log a x = n
n is called the logarithm of x to base a.

• logarithm of multiplication of two numbers is equal to sum of the logarithm of the two numbers log (pq) = log p + log q

• logarithm of fraction of two numbers is equal to the difference of the logarithms of the two numbers log (p/q) = log p – log q

• log a (p)n = n log a p

• a (log a p ) = p

Important rule on change of base in logarithms:
• log a b = (log n b)/(log n a)

Common Logarithms:

Logarithms expressed or calculated to base 10 are called Common Logarithms

Example:
Log x 10

Characteristic and Mantissa:

Example:
log 10 15 = 1.176 = 1 + 0.176

in the sum on the right, the integral part 1 is called Characteristic and the fractional part 0.176 is called Mantissa.

How to find the Characteristic of the logarithm of a Number:

The characteristic (in the logarithm of a number) is one more than the number of zeroes to the right of the decimal in a positive number less than 1

Properties of the Mantissa:

The mantissa is same for the same order of digits in two different numbers, irrespective of where the decimal point is in the two numbers

How to find the Mantissa :

The Mantissa of the logarithm of numbers is found using logarithm tables.

What is Antilogarithm?

log 10 15 = 1.176 1.176 is called the antilog of 15 to base 10.