#### The Logarithmic Function

- The logarithmic function with base is defined as follows:

a^{x} = b is equivalent to log_{a}{b}=x, where a \in R^{+}\setminus \left \{ 1 \right \} .

Note: ‘a \in R^{+}\setminus \left \{ 1 \right \}‘ means that could be any positive number, excluding 1.

- The expression log_{a}{y}=x is read as: ‘the logarithm of y to the base a is equal to x’.

Example