As you know, multiplication is a shortcut for addition.
Let “a” be a positive real number and a ≠1.
The function f: (0, ∝) →R is defined by
f(x) = logax,∀ x ∈(0, ∝) is called a logarithmic function.
If logax = logay ⇒ x = y
The logarithms computed to the base
e = 2.718 . . . are called natural logarithms (Napierian).
This can be written as logex (lnx)
The logarithms computed to the base 10 are called common (Briggs) logarithms and can be written as log10x.
- The domain of the logarithmic function = set of positive real numbers (0,∝)
- Range = set of real numbers (–∝ , ∝).
- If (a > 1, n >1) or (0 < n < 1, 0 < a < 1)
then logan > 0
- If (n > 1, 0 < a < 1) or (0 < n < 1, a > 1)
then logan < 0
Try these questions
- log10x is an example of:
- Briggs logarithm
- Napierian logarithm
- Uncommon logarithm
- Natural logarithm
- Napierian logarithm is written as: