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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

1. Napierian logarithm is written as:

2. -∝

3. lnx

4. log10x