# Introduction to logarithms form

Consider the three numbers m, n and x are related such that

Then n is called the logarithm of the number 'x' to the base 'm' and is written as log_{m} x = n

We can write natural logarithms as:

To mean log_{e}x (that is log x to the base e)

The number e is an irrational constant and its value is 2.718281828......

**Logarithms Form with their Property:**

**For base form:**

Get the log of the quarrel divided through the log of the base.

log_{a} x = ( log_{b} x ) / ( log_{b} a ).

log_{b} x = ( log x ) / ( log b ) = ( ln x ) / ( ln b ).

**For inverse:**** **

The inverse is obtained by taking the base a logarithm of both sides of the exponential equation.

x = a^{y}

log_{a}(x) = log_{a}(a^{y})

log_{a}(x) = y

In the above step the log_{a}(a) cancels and the equation becomes as we seen above.

Inverse Properties of Logs

Since logs and exponents cancel each other we have:

e^{ln x }= x

And in e^{x} = x

**General properties of logarithm forms:**

log_{a (}m X n) = log_{a} m + log_{a} n

log_{a } = log_{a} m - log_{a} n

log_{a} = n log_{a} m

log _{a} = log _{a} = log_{a} m

log _{a} x = log _{b} x . log _{a} b

Logarithm of unity to any base( 1) is zero.

log_{a }1 = 0 ( since =1)

**Note:
1. **log

_{10 }1 = 0

**2.**log

_{5 }1 = 0

**.**

Logarithm of positive number to the same base is equal to 1

log _{a} a = 1 ( since =a)

**Note **

1. log_{ 3} 3 = 1

2. log _{10} 10 = 1

It is to be written as antilog_{2} 5 = 32

Hence 2^{5} = 32 log_{2} 32 = 5 antilog_{2 }5 = 32

5^{4} = 625 log_{5} 625 = 4 antilog_{5 }4 = 625

# ###SUB-TOPIC###Examples for Logarithm Forms ###

Log 756.8

The characteristic is calculated as= 3-1 = 2

To find the mantissa, refer the logarithm table.

First neglect the decimal point, the obtained number is 7 568.

Search the number 75 in the extreme left-hand column of the logarithm table.

log 756.8 = 2.8790 (8785 + 5 = 8790)

Similarly, log 75.68 = 1.8790

log .075 68 = -2 + .8790