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Other logarithms

Logarithmic Functions

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
 

Natural logarithms

The logarithms computed to the base

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

This can be written as logex (lnx)
 

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 logan > 0

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

  4. log10x

 
Answer: B
 

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