Logarithm Notes Part-1
- Logarithm:
If a is a positive real number,
other than 1 and am = x, then we write:
m = logax and we say that the value of log x to the base a is m.
2. Common Logarithms:
Logarithms to the base 10 are known as
common logarithms.m = logax and we say that the value of log x to the base a is m.
2. Common Logarithms:
Characteristic:
The internal part of the logarithm of a
number is called its characteristic.
Case I: When the number is greater than 1.
In this case, the characteristic is one
less than the number of digits in the left of the decimal point in the given
number.
Case II: When the number is less than 1.
In this case, the characteristic is one
more than the number of zeros between the decimal point and the first
significant digit of the number and it is negative.
Instead of -1, -2 etc. we write 1
(one bar), 2 (two bar), etc.
Examples:-
Number
|
Characteristic
|
Number
|
Characteristic
|
654.24
|
2
|
0.6453
|
1
|
26.649
|
1
|
0.06134
|
2
|
8.3547
|
0
|
0.00123
|
3
|
Mantissa:
The decimal part of the logarithm of a
number is known is its mantissa. For mantissa, we look through log
table.
Logarithm :
If a is a positive real number, other than
1 and am = x, then we write m = loga x and we say that the value of log x to
the base a is m.
Examples
:
1. 103 1000 = log10 1000 = 3.
2. Common Logarithms :
Logarithms to the base 10 are known as
common logarithms.
Properties of Logarithms :
1. loga(xy) =
loga x + loga y
2. loga(x / y) = loga
x - loga y
3. logx x = 1
4. loga 1 = 0
5. loga (xp) =
p(loga x )
6. loga x = 1 /
logxa