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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
 

 

 





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