Logarithm of a negative number or zero is not defined.
Natural logarithm: Base of the number is ‘e’.
Common logarithm: Base of the number is 10. When the base is not mentioned, it can be taken as 10.
Properties of logarithm:
- loga1 = 0
- logaa = 1
- logaxy = logax + logay
- loga(X/Y) = logaX – logaY
- logab × logba = 1
- blogbx = x
- logax = 1/logxa
- logab = logcb × logac
- logabc = c × logab
- xlogby = ylogbx
- If 0 < a < 1, then logax < logay (if x > y)
- If a > 1, then logax > logay (if x > y)
SOME POINTS TO REMEMBER:
- log(x – y) ≠ logx – logy
- log(x + y) ≠ logx + logy
Log values of some numbers (base 10)
Number | Value |
1 | 0 |
2 | 0.301 |
3 | 0.4771 |
4 | 0.602 |
5 | 0.698 |
6 | 0.778 |
7 | 0.845 |
8 | 0.903 |
9 | 0.954 |
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