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 ).
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)
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)
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 ###
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