Precalculus Examples

$y = \log_{a} (x)$

Step 1

Set the base in $\log_{a} (x)$ greater than $0$ to find where the expression is defined.

$a > 0$

Step 2

Set the argument in $\log_{a} (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

Step 3

Set the base in $\log_{a} (x)$ equal to $1$ to find where the expression is undefined.

$a = 1$

Step 4

The domain is all values of $a$ that make the expression defined.

Interval Notation:

$(0, 1) \cup (1, \infty)$

Set-Builder Notation:

${a | a > 0, a \neq 1}$