**What you will learn in Logarithms? **

In exponents, how do we write 2 to the power of 3?

2^{3} = 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.

**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 2^{3} = 8, then log _{2} 8 = 3

if a^{n} = 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)

Logarithms expressed or calculated to base 10 are called Common Logarithms

*Example: *

Log _{x} 10

*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

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

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

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

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