# How do you find the domain and range of y = log_2(x - 3)?

Jun 21, 2015

The argument of a log-function must be positive.

#### Explanation:

This means $x - 3 > 0 \to x > 3$

If $x$ gets closer to $3$, the log will get more and more negative

Or, in the "language""
${\lim}_{x \to 3} {\log}_{2} \left(x - 3\right) = - \infty$

The other way, $x$ getting larger, will get the function larger:
${\lim}_{x \to \infty} {\log}_{2} \left(x - 3\right) = \infty$