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 a^x = n is exponential form, then
log _a n = x is the logarithmic form.

This lesson will cover Logarithms in detail.

If you wish to set off with Logarithm lesson, then click on any of the links below:
1. Definition of Logarithm
2 .Problems on Logarithms into Exponentials
3. The Four important Laws of Logarithms (or) Logarithm Rules :
4.Problems on Logarithm Rules
5. Important rule on change of base in logarithms:
6. Rule of Base Change:
7.Common Logarithms:
8. Characteristic and Mantissa
9. How to find the Characteristic of the logarithm of a Number?
10. Properties of Mantissa
11. How to find the Mantissa?
12. What is Antilogarithm?
13. Solved Examples

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.

The Four important Laws of Logarithms:

• 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.