Logarithmic Functions

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) = log_ax,∀ x ∈(0, ∝) is called a logarithmic function.

If logax = log_ay ⇒ x = y

Natural logarithms

The logarithms computed to the base

e = 2.718 . . . are called natural logarithms (Napierian).

This can be written as log_ex (l_nx)

Common logarithms

The logarithms computed to the base 10 are called common (Briggs) logarithms and can be written as log10x.

1. The domain of the logarithmic function = set of positive real numbers (0,∝)
2. Range = set of real numbers (–∝ , ∝).

Logarithmic symbols

1. If (a > 1, n >1) or (0 < n < 1, 0 < a < 1)
                               then log_an > 0


2. If (n > 1, 0 < a < 1) or (0 < n < 1, a > 1)
                               then log_an < 0

Try these questions

1. log10x is an example of:
2. Briggs logarithm
3. Napierian logarithm
4. Uncommon logarithm
5. Natural logarithm

Answer: A

1. Napierian logarithm is written as:
2. -∝
3. l_nx
4. log₁₀x
5. ∝

Answer: B