Finite Math Examples

$\log (2 + x) - \log (x - 3) = \log (2)$

Step 1

Set the argument in $\log (2 + x)$ greater than $0$ to find where the expression is defined.

$2 + x > 0$

Step 2

Subtract $2$ from both sides of the inequality.

$x > - 2$

Step 3

Set the argument in $\log (x - 3)$ greater than $0$ to find where the expression is defined.

$x - 3 > 0$

Step 4

Add $3$ to both sides of the inequality.

$x > 3$

Step 5

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

Interval Notation:

$(3, \infty)$

Set-Builder Notation:

${x | x > 3}$

Step 6