what is the range of this logarithmic function?

Explanation:

Step1: Recall range definition

The range of a function is the set of all possible output - values (y - values).

Step2: Analyze the graph

For a logarithmic function, as seen in the graph, the y - values can take on any real number. The function extends infinitely upwards and downwards along the y - axis.

Answer:

All real numbers, or $(-\infty,\infty)$