Finite Math Examples

$\log_{x} (27) = - 3$

Step 1

Set the base in $\log_{x} (27)$ greater than $0$ to find where the expression is defined.

$x > 0$

Step 2

Set the base in $\log_{x} (27)$ equal to $1$ to find where the expression is undefined.

$x = 1$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

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

Step 4