Graph of Logarithmic Function

For x (0, ), the value of log x is uniquely defined.For x (0, ), the value of log x is uniquely defined.

\ x g log x is a well-defined function from (0, ) to (-, ). The value of e to one place of decimal is 2.7. The approximate values of the function log x for some of the values of x are as follows:

We see that as x increases from 0 to , the value of log x also increases indefinitely. The function log x is one-one.