Definition: Logarithm is a quantity which represents a number, which is a power to a fixed number, which is required to produce a given number.
Generally the logarithm is expressed in the following form:
R = loga x
Here,
‘a’ is called base
‘X’ is fixed number
‘R’ is required power to produce the ‘X’. [aR = X]
Here, ‘R’ is the number, which is actually the power of ‘a’, which will produce the given number ‘X’. For example, let’s consider,
a = 10
X = 1000
Now, to produce 1000 (value of X), we need to raise the power of ‘a’ to 3. Because, 103 = 1000. In equation form, we can write:
aR = X , which implies, 103 = 1000, where R=3, a = 10 and X = 1000.
In logarithm, we find out the ‘R’, means the required power to produce ‘X’, which is 1000 in this case.
Example:
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| Numeric Expression | aR = X from | Logarithmic form
R = loga x
|
| 103 = 1000 | a = 10, R = 3, X = 1000 | log10 1000
=log10 103 =3 |
| 34 = 81 | a = 3, R = 4, X = 81 | log3 81
=log3 34 = 4 |
| 2-3 = |
a = 2, R = -3, X = |
log2 ( =log2 2-3 = -3 |
| (0.1)2 = 0.01 | a = 0.1, R = 2, X = 0.01 | log0.1 0.01
=log0.1 (0.1)2 =2 log0.1 (0.1) = 2 |