## 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.

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 the multiplication of two numbers is equal to the 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 the 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.