# 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 logm x =  n

We can write natural logarithms as:

To mean logex (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.

loga x = ( logb x ) / ( logb a ).

logb 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 = ay

loga(x) = loga(ay)

loga(x) = y

In the above step the loga(a) cancels and the equation becomes as we seen above.

Inverse Properties of Logs

Since logs and exponents cancel each other we have:

eln x  =  x

And in ex = x

General properties of logarithm forms:

loga (m X n) = loga m + loga n

loga  = loga m   -  loga n

loga  = n loga m

log a  = log a   =  loga m

log a x = log b x . log a b

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

loga 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 antilog2 5 = 32

Hence 25 = 32  log2 32 = 5    antilog2 5   =  32

54 = 625  log5 625 = 4    antilog5 4   =  625

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

Example

Log 756.8

Solution

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