Return to Assignments Logarithmic functions and graphs

### Assignment 4

Under which conditions is the following logarithmic function defined?

### Solution

First the base has to satisfy:

and

so:

and

Further the argument has to satisfy:

The graph of the function at the left-hand side is an 'opens up' parabola and the function can be factorized:

The parabola lies above the -axis if:

or

and for these values of the logarithm is defined.